Chapter 4 of Class 7 Maths deals with Simple Equations, a fundamental concept that introduces students to algebra. Simple equations contain only one variable and can be solved by basic arithmetic operations such as addition, subtraction, multiplication, and division. Solving these equations enhances problem-solving skills and sets the stage for more complex algebraic concepts. In this blog post, we will go through all the exercises in Chapter 4 and provide solutions to every problem. Additionally, we will include more related questions to ensure that you gain a complete understanding of the topic.
Exercise 4.1: Introduction to Simple Equations
- Solve the equation:
- x+5=10x + 5 = 10x+5=10
To solve for xxx, subtract 5 from both sides of the equation:
x=10−5x = 10 – 5x=10−5
x=5x = 5x=5
The solution is x=5x = 5x=5. - Solve the equation:
- y−3=7y – 3 = 7y−3=7
To solve for yyy, add 3 to both sides:
y=7+3y = 7 + 3y=7+3
y=10y = 10y=10
The solution is y=10y = 10y=10. - Solve the equation:
- 3z=153z = 153z=15
To solve for zzz, divide both sides by 3:
z=153z = \frac{15}{3}z=315
z=5z = 5z=5
The solution is z=5z = 5z=5.
Exercise 4.2: Solving Equations Involving Multiplication and Division
- Solve the equation:
- 2x=122x = 122x=12
To solve for xxx, divide both sides by 2:
x=122x = \frac{12}{2}x=212
x=6x = 6x=6
The solution is x=6x = 6x=6. - Solve the equation:
- y4=5\frac{y}{4} = 54y=5
To solve for yyy, multiply both sides by 4:
y=5×4y = 5 \times 4y=5×4
y=20y = 20y=20
The solution is y=20y = 20y=20. - Solve the equation:
- z3=9\frac{z}{3} = 93z=9
To solve for zzz, multiply both sides by 3:
z=9×3z = 9 \times 3z=9×3
z=27z = 27z=27
The solution is z=27z = 27z=27.
Exercise 4.3: Solving Equations by Transposing Terms
- Solve the equation:
- x+7=12x + 7 = 12x+7=12
To solve for xxx, subtract 7 from both sides:
x=12−7x = 12 – 7x=12−7
x=5x = 5x=5
The solution is x=5x = 5x=5. - Solve the equation:
- 5y−4=165y – 4 = 165y−4=16
First, add 4 to both sides:
5y=16+45y = 16 + 45y=16+4
5y=205y = 205y=20
Now, divide both sides by 5:
y=205y = \frac{20}{5}y=520
y=4y = 4y=4
The solution is y=4y = 4y=4. - Solve the equation:
- 2z+6=202z + 6 = 202z+6=20
First, subtract 6 from both sides:
2z=20−62z = 20 – 62z=20−6
2z=142z = 142z=14
Now, divide both sides by 2:
z=142z = \frac{14}{2}z=214
z=7z = 7z=7
The solution is z=7z = 7z=7.
Exercise 4.4: Word Problems Involving Simple Equations
- A number is added to 8 and the result is 15. Find the number.Solution:
Let the number be xxx. The equation is:
x+8=15x + 8 = 15x+8=15
To solve for xxx, subtract 8 from both sides:
x=15−8x = 15 – 8x=15−8
x=7x = 7x=7
The number is 7. - The sum of a number and 5 is equal to 12. Find the number.Solution:
Let the number be yyy. The equation is:
y+5=12y + 5 = 12y+5=12
To solve for yyy, subtract 5 from both sides:
y=12−5y = 12 – 5y=12−5
y=7y = 7y=7
The number is 7. - A number is multiplied by 6 and the result is 54. Find the number.Solution:
Let the number be zzz. The equation is:
6z=546z = 546z=54
To solve for zzz, divide both sides by 6:
z=546z = \frac{54}{6}z=654
z=9z = 9z=9
The number is 9.
Exercise 4.5: Solving Equations Involving Parentheses
- Solve the equation:
- 2(x+3)=142(x + 3) = 142(x+3)=14
First, distribute 2 to both terms inside the parentheses:
2x+6=142x + 6 = 142x+6=14
Now, subtract 6 from both sides:
2x=14−62x = 14 – 62x=14−6
2x=82x = 82x=8
Finally, divide both sides by 2:
x=82x = \frac{8}{2}x=28
x=4x = 4x=4
The solution is x=4x = 4x=4. - Solve the equation:
- 3(y−2)=183(y – 2) = 183(y−2)=18
First, distribute 3 to both terms inside the parentheses:
3y−6=183y – 6 = 183y−6=18
Now, add 6 to both sides:
3y=18+63y = 18 + 63y=18+6
3y=243y = 243y=24
Finally, divide both sides by 3:
y=243y = \frac{24}{3}y=324
y=8y = 8y=8
The solution is y=8y = 8y=8.
Exercise 4.6: Solving Multi-Step Equations
- Solve the equation:
- 3(x−4)=123(x – 4) = 123(x−4)=12
First, distribute 3 to both terms inside the parentheses:
3x−12=123x – 12 = 123x−12=12
Now, add 12 to both sides:
3x=12+123x = 12 + 123x=12+12
3x=243x = 243x=24
Finally, divide both sides by 3:
x=243x = \frac{24}{3}x=324
x=8x = 8x=8
The solution is x=8x = 8x=8. - Solve the equation:
- 2(y+5)−6=102(y + 5) – 6 = 102(y+5)−6=10
First, distribute 2 to both terms inside the parentheses:
2y+10−6=102y + 10 – 6 = 102y+10−6=10
Now, combine like terms:
2y+4=102y + 4 = 102y+4=10
Subtract 4 from both sides:
2y=10−42y = 10 – 42y=10−4
2y=62y = 62y=6
Finally, divide both sides by 2:
y=62y = \frac{6}{2}y=26
y=3y = 3y=3
The solution is y=3y = 3y=3.
Exercise 4.7: Equations with Variables on Both Sides
- Solve the equation:
- 3x+5=2x+103x + 5 = 2x + 103x+5=2x+10
First, subtract 2x2x2x from both sides:
x+5=10x + 5 = 10x+5=10
Now, subtract 5 from both sides:
x=10−5x = 10 – 5x=10−5
x=5x = 5x=5
The solution is x=5x = 5x=5. - Solve the equation:
- 4y−3=2y+94y – 3 = 2y + 94y−3=2y+9
First, subtract 2y2y2y from both sides:
2y−3=92y – 3 = 92y−3=9
Now, add 3 to both sides:
2y=9+32y = 9 + 32y=9+3
2y=122y = 122y=12
Finally, divide both sides by 2:
y=122y = \frac{12}{2}y=212
y=6y = 6y=6
The solution is y=6y = 6y=6.
Additional Questions:
- Solve the equation:
- 5x−10=205x – 10 = 205x−10=20
Add 10 to both sides:
5x=20+105x = 20 + 105x=20+10
5x=305x = 305x=30
Divide both sides by 5:
x=305x = \frac{30}{5}x=530
x=6x = 6x=6
The solution is x=6x = 6x=6. - Solve the equation:
- 6(y+2)=306(y + 2) = 306(y+2)=30
First, distribute 6 to both terms inside the parentheses:
6y+12=306y + 12 = 306y+12=30
Subtract 12 from both sides:
6y=30−126y = 30 – 126y=30−12
6y=186y = 186y=18
Divide both sides by 6:
y=186y = \frac{18}{6}y=618
y=3y = 3y=3
The solution is y=3y = 3y=3.
Additional Practice Questions:
- Solve the equation:
2x+3=92x + 3 = 92x+3=9 - Solve the equation:
5y−4=215y – 4 = 215y−4=21 - Solve the equation:
7z+6=347z + 6 = 347z+6=34 - Solve the equation:
3(x−2)=183(x – 2) = 183(x−2)=18 - Solve the equation:
4y+12=284y + 12 = 284y+12=28 - Solve the equation:
2z−4=102z – 4 = 102z−4=10 - Solve the equation:
6x+8=266x + 8 = 266x+8=26 - Solve the equation:
3y+7=223y + 7 = 223y+7=22 - Solve the equation:
x4=3\frac{x}{4} = 34x=3 - Solve the equation:
5(x+2)=305(x + 2) = 305(x+2)=30 - Solve the equation:
4y−6=184y – 6 = 184y−6=18 - Solve the equation:
3z+8=173z + 8 = 173z+8=17 - Solve the equation:
5×3=15\frac{5x}{3} = 1535x=15 - Solve the equation:
2x−7=112x – 7 = 112x−7=11 - Solve the equation:
9y+5=239y + 5 = 239y+5=23 - Solve the equation:
7z−4=317z – 4 = 317z−4=31 - Solve the equation:
4×5=16\frac{4x}{5} = 1654x=16 - Solve the equation:
2y+5=152y + 5 = 152y+5=15 - Solve the equation:
6z−2=226z – 2 = 226z−2=22 - Solve the equation:
5x+8=335x + 8 = 335x+8=33 - Solve the equation:
3y−4=173y – 4 = 173y−4=17 - Solve the equation:
4z+9=254z + 9 = 254z+9=25 - Solve the equation:
6(x−3)=246(x – 3) = 246(x−3)=24 - Solve the equation:
2y+3=132y + 3 = 132y+3=13 - Solve the equation:
5z−6=245z – 6 = 245z−6=24 - Solve the equation:
8×2=16\frac{8x}{2} = 1628x=16 - Solve the equation:
4y+5=174y + 5 = 174y+5=17 - Solve the equation:
9z−10=509z – 10 = 509z−10=50 - Solve the equation:
7x+3=257x + 3 = 257x+3=25 - Solve the equation:
3(y+4)=213(y + 4) = 213(y+4)=21
Below are the solutions to each of the 30 equations:
1. Solve the equation:
2x + 3 = 9
Solution:
Subtract 3 from both sides:
2x=9−32x = 9 – 32x=9−3
2x=62x = 62x=6
Now divide both sides by 2:
x=62x = \frac{6}{2}x=26
x=3x = 3x=3
2. Solve the equation:
5y – 4 = 21
Solution:
Add 4 to both sides:
5y=21+45y = 21 + 45y=21+4
5y=255y = 255y=25
Now divide both sides by 5:
y=255y = \frac{25}{5}y=525
y=5y = 5y=5
3. Solve the equation:
7z + 6 = 34
Solution:
Subtract 6 from both sides:
7z=34−67z = 34 – 67z=34−6
7z=287z = 287z=28
Now divide both sides by 7:
z=287z = \frac{28}{7}z=728
z=4z = 4z=4
4. Solve the equation:
3(x – 2) = 18
Solution:
Distribute 3 to both terms inside the parentheses:
3x−6=183x – 6 = 183x−6=18
Now, add 6 to both sides:
3x=18+63x = 18 + 63x=18+6
3x=243x = 243x=24
Divide both sides by 3:
x=243x = \frac{24}{3}x=324
x=8x = 8x=8
5. Solve the equation:
4y + 12 = 28
Solution:
Subtract 12 from both sides:
4y=28−124y = 28 – 124y=28−12
4y=164y = 164y=16
Now divide both sides by 4:
y=164y = \frac{16}{4}y=416
y=4y = 4y=4
6. Solve the equation:
2z – 4 = 10
Solution:
Add 4 to both sides:
2z=10+42z = 10 + 42z=10+4
2z=142z = 142z=14
Now divide both sides by 2:
z=142z = \frac{14}{2}z=214
z=7z = 7z=7
7. Solve the equation:
6x + 8 = 26
Solution:
Subtract 8 from both sides:
6x=26−86x = 26 – 86x=26−8
6x=186x = 186x=18
Now divide both sides by 6:
x=186x = \frac{18}{6}x=618
x=3x = 3x=3
8. Solve the equation:
3y + 7 = 22
Solution:
Subtract 7 from both sides:
3y=22−73y = 22 – 73y=22−7
3y=153y = 153y=15
Now divide both sides by 3:
y=153y = \frac{15}{3}y=315
y=5y = 5y=5
9. Solve the equation:
x/4 = 3
Solution:
Multiply both sides by 4:
x=3×4x = 3 \times 4x=3×4
x=12x = 12x=12
10. Solve the equation:
5(x + 2) = 30
Solution:
Distribute 5 to both terms inside the parentheses:
5x+10=305x + 10 = 305x+10=30
Subtract 10 from both sides:
5x=30−105x = 30 – 105x=30−10
5x=205x = 205x=20
Now divide both sides by 5:
x=205x = \frac{20}{5}x=520
x=4x = 4x=4
11. Solve the equation:
4y – 6 = 18
Solution:
Add 6 to both sides:
4y=18+64y = 18 + 64y=18+6
4y=244y = 244y=24
Now divide both sides by 4:
y=244y = \frac{24}{4}y=424
y=6y = 6y=6
12. Solve the equation:
3z + 8 = 17
Solution:
Subtract 8 from both sides:
3z=17−83z = 17 – 83z=17−8
3z=93z = 93z=9
Now divide both sides by 3:
z=93z = \frac{9}{3}z=39
z=3z = 3z=3
13. Solve the equation:
5x/3 = 15
Solution:
Multiply both sides by 3:
5x=15×35x = 15 \times 35x=15×3
5x=455x = 455x=45
Now divide both sides by 5:
x=455x = \frac{45}{5}x=545
x=9x = 9x=9
14. Solve the equation:
2x – 7 = 11
Solution:
Add 7 to both sides:
2x=11+72x = 11 + 72x=11+7
2x=182x = 182x=18
Now divide both sides by 2:
x=182x = \frac{18}{2}x=218
x=9x = 9x=9
15. Solve the equation:
9y + 5 = 23
Solution:
Subtract 5 from both sides:
9y=23−59y = 23 – 59y=23−5
9y=189y = 189y=18
Now divide both sides by 9:
y=189y = \frac{18}{9}y=918
y=2y = 2y=2
16. Solve the equation:
7z – 4 = 31
Solution:
Add 4 to both sides:
7z=31+47z = 31 + 47z=31+4
7z=357z = 357z=35
Now divide both sides by 7:
z=357z = \frac{35}{7}z=735
z=5z = 5z=5
17. Solve the equation:
4x/5 = 16
Solution:
Multiply both sides by 5:
4x=16×54x = 16 \times 54x=16×5
4x=804x = 804x=80
Now divide both sides by 4:
x=804x = \frac{80}{4}x=480
x=20x = 20x=20
18. Solve the equation:
2y + 5 = 15
Solution:
Subtract 5 from both sides:
2y=15−52y = 15 – 52y=15−5
2y=102y = 102y=10
Now divide both sides by 2:
y=102y = \frac{10}{2}y=210
y=5y = 5y=5
19. Solve the equation:
6z – 2 = 22
Solution:
Add 2 to both sides:
6z=22+26z = 22 + 26z=22+2
6z=246z = 246z=24
Now divide both sides by 6:
z=246z = \frac{24}{6}z=624
z=4z = 4z=4
20. Solve the equation:
5x + 8 = 33
Solution:
Subtract 8 from both sides:
5x=33−85x = 33 – 85x=33−8
5x=255x = 255x=25
Now divide both sides by 5:
x=255x = \frac{25}{5}x=525
x=5x = 5x=5
21. Solve the equation:
3y – 4 = 17
Solution:
Add 4 to both sides:
3y=17+43y = 17 + 43y=17+4
3y=213y = 213y=21
Now divide both sides by 3:
y=213y = \frac{21}{3}y=321
y=7y = 7y=7
22. Solve the equation:
4z + 9 = 25
Solution:
Subtract 9 from both sides:
4z=25−94z = 25 – 94z=25−9
4z=164z = 164z=16
Now divide both sides by 4:
z=164z = \frac{16}{4}z=416
z=4z = 4z=4
23. Solve the equation:
6(x – 3) = 24
Solution:
Distribute 6 to both terms inside the parentheses:
6x−18=246x – 18 = 246x−18=24
Add 18 to both sides:
6x=24+186x = 24 + 186x=24+18
6x=426x = 426x=42
Now divide both sides by 6:
x=426x = \frac{42}{6}x=642
x=7x = 7x=7
24. Solve the equation:
2y + 3 = 13
Solution:
Subtract 3 from both sides:
2y=13−32y = 13 – 32y=13−3
2y=102y = 102y=10
Now divide both sides by 2:
y=102y = \frac{10}{2}y=210
y=5y = 5y=5
25. Solve the equation:
5z – 6 = 24
Solution:
Add 6 to both sides:
5z=24+65z = 24 + 65z=24+6
5z=305z = 305z=30
Now divide both sides by 5:
z=305z = \frac{30}{5}z=530
z=6z = 6z=6
26. Solve the equation:
8x/2 = 16
Solution:
Multiply both sides by 2:
8x=16×28x = 16 \times 28x=16×2
8x=328x = 328x=32
Now divide both sides by 8:
x=328x = \frac{32}{8}x=832
x=4x = 4x=4
27. Solve the equation:
4y + 5 = 17
Solution:
Subtract 5 from both sides:
4y=17−54y = 17 – 54y=17−5
4y=124y = 124y=12
Now divide both sides by 4:
y=124y = \frac{12}{4}y=412
y=3y = 3y=3
28. Solve the equation:
9z – 10 = 50
Solution:
Add 10 to both sides:
9z=50+109z = 50 + 109z=50+10
9z=609z = 609z=60
Now divide both sides by 9:
z=609z = \frac{60}{9}z=960
z=203z = \frac{20}{3}z=320 (approx. z=6.67z = 6.67z=6.67)
29. Solve the equation:
7x + 3 = 25
Solution:
Subtract 3 from both sides:
7x=25−37x = 25 – 37x=25−3
7x=227x = 227x=22
Now divide both sides by 7:
x=227x = \frac{22}{7}x=722
x≈3.14x \approx 3.14x≈3.14
30. Solve the equation:
3(y + 4) = 21
Solution:
Distribute 3 to both terms inside the parentheses:
3y+12=213y + 12 = 213y+12=21
Subtract 12 from both sides:
3y=21−123y = 21 – 123y=21−12
3y=93y = 93y=9
Now divide both sides by 3:
y=93y = \frac{9}{3}y=39
y=3y = 3y=3
These solutions should help you practice solving various types of simple equations. Keep practicing to strengthen your skills!
Class 7 Maths – Chapter 3: Fractions and Decimals Solutions
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Sidhant Singh is a highly accomplished professional educator with a diverse academic background. He holds a Master’s degree in History, an MSc in Electrical Engineering and a PhD, demonstrating his extensive knowledge and expertise in both the humanities and the sciences. His unique combination of skills enables him to offer a well-rounded perspective in his teaching and research, making him a valuable resource for students across various fields.