In Class 7, Chapter 5 of Maths typically focuses on Simple Equations. This chapter helps students understand how to solve equations where the variable is unknown. The skills acquired in this chapter lay the foundation for higher-level algebraic equations. In this blog post, we will go through all the exercises and solutions in a step-by-step manner, making it easier to grasp the concepts and solve the problems confidently.
Let’s dive into the worksheet and explore how to approach each question.
Maths Exercise 5.1: Solving Simple Equations
Q1. Solve the equation:
2x=102x = 102x=10
Solution:
To solve for xxx, divide both sides of the equation by 2:x=102=5x = \frac{10}{2} = 5x=210=5
So, the solution is x=5x = 5x=5.
Q2. Solve the equation:
3x+4=193x + 4 = 193x+4=19
Solution:
First, subtract 4 from both sides:3x=19−43x = 19 – 43x=19−43x=153x = 153x=15
Now, divide both sides by 3:x=153=5x = \frac{15}{3} = 5x=315=5
So, the solution is x=5x = 5x=5.
Exercise 5.2: Solving Equations Involving Fractions
Q1. Solve the equation:
x4=5\frac{x}{4} = 54x=5
Solution:
Multiply both sides by 4 to isolate xxx:x=5×4x = 5 \times 4x=5×4x=20x = 20x=20
So, the solution is x=20x = 20x=20.
Q2. Solve the equation:
3×5=12\frac{3x}{5} = 1253x=12
Solution:
Multiply both sides by 5:3x=12×53x = 12 \times 53x=12×53x=603x = 603x=60
Now, divide both sides by 3:x=603=20x = \frac{60}{3} = 20x=360=20
So, the solution is x=20x = 20x=20.
Exercise 5.3: Word Problems on Simple Equations
Q1. The sum of a number and 7 is 15. Find the number.
Solution:
Let the number be xxx. According to the problem, the equation would be:x+7=15x + 7 = 15x+7=15
Now, subtract 7 from both sides:x=15−7x = 15 – 7x=15−7x=8x = 8x=8
So, the number is 888.
Q2. A number subtracted from 12 gives 5. Find the number.
Solution:
Let the number be xxx. According to the problem, the equation is:12−x=512 – x = 512−x=5
Now, subtract 5 from both sides:12−5=x12 – 5 = x12−5=xx=7x = 7x=7
So, the number is 777.
Exercise 5.4: More Challenging Equations
Q1. Solve the equation:
4(x+2)=204(x + 2) = 204(x+2)=20
Solution:
First, expand the left side:4x+8=204x + 8 = 204x+8=20
Now, subtract 8 from both sides:4x=20−84x = 20 – 84x=20−84x=124x = 124x=12
Now, divide both sides by 4:x=124=3x = \frac{12}{4} = 3x=412=3
So, the solution is x=3x = 3x=3.
Q2. Solve the equation:
5x−3=2x+95x – 3 = 2x + 95x−3=2x+9
Solution:
First, move the terms involving xxx to one side of the equation:5x−2x=9+35x – 2x = 9 + 35x−2x=9+33x=123x = 123x=12
Now, divide both sides by 3:x=123=4x = \frac{12}{3} = 4x=312=4
So, the solution is x=4x = 4x=4.
Practice Questions:
These 30 additional practice questions should provide plenty of exercises to solidify your understanding of solving simple equations. Keep practicing, and don’t hesitate to reach out if you need further explanations!
1. Solve the equation:
4x=324x = 324x=32
Solution:
Divide both sides by 4:x=324=8x = \frac{32}{4} = 8x=432=8
2. Solve the equation:
3x−7=113x – 7 = 113x−7=11
Solution:
Add 7 to both sides:3x=11+7=183x = 11 + 7 = 183x=11+7=18
Now, divide by 3:x=183=6x = \frac{18}{3} = 6x=318=6
3. Solve the equation:
2x+5=132x + 5 = 132x+5=13
Solution:
Subtract 5 from both sides:2x=13−5=82x = 13 – 5 = 82x=13−5=8
Now, divide by 2:x=82=4x = \frac{8}{2} = 4x=28=4
4. Solve the equation:
5x−3=125x – 3 = 125x−3=12
Solution:
Add 3 to both sides:5x=12+3=155x = 12 + 3 = 155x=12+3=15
Now, divide by 5:x=155=3x = \frac{15}{5} = 3x=515=3
5. Solve the equation:
6x+9=216x + 9 = 216x+9=21
Solution:
Subtract 9 from both sides:6x=21−9=126x = 21 – 9 = 126x=21−9=12
Now, divide by 6:x=126=2x = \frac{12}{6} = 2x=612=2
6. Solve the equation:
3(x+4)=213(x + 4) = 213(x+4)=21
Solution:
Expand the left side:3x+12=213x + 12 = 213x+12=21
Subtract 12 from both sides:3x=21−12=93x = 21 – 12 = 93x=21−12=9
Now, divide by 3:x=93=3x = \frac{9}{3} = 3x=39=3
7. Solve the equation:
x5=6\frac{x}{5} = 65x=6
Solution:
Multiply both sides by 5:x=6×5=30x = 6 \times 5 = 30x=6×5=30
8. Solve the equation:
2×3=4\frac{2x}{3} = 432x=4
Solution:
Multiply both sides by 3:2x=4×3=122x = 4 \times 3 = 122x=4×3=12
Now, divide by 2:x=122=6x = \frac{12}{2} = 6x=212=6
9. Solve the equation:
5(x−2)=305(x – 2) = 305(x−2)=30
Solution:
Expand the left side:5x−10=305x – 10 = 305x−10=30
Add 10 to both sides:5x=30+10=405x = 30 + 10 = 405x=30+10=40
Now, divide by 5:x=405=8x = \frac{40}{5} = 8x=540=8
10. Solve the equation:
x+15=28x + 15 = 28x+15=28
Solution:
Subtract 15 from both sides:x=28−15=13x = 28 – 15 = 13x=28−15=13
11. Solve the equation:
7x−5=307x – 5 = 307x−5=30
Solution:
Add 5 to both sides:7x=30+5=357x = 30 + 5 = 357x=30+5=35
Now, divide by 7:x=357=5x = \frac{35}{7} = 5x=735=5
12. Solve the equation:
9x=729x = 729x=72
Solution:
Divide both sides by 9:x=729=8x = \frac{72}{9} = 8x=972=8
13. Solve the equation:
x−8=10x – 8 = 10x−8=10
Solution:
Add 8 to both sides:x=10+8=18x = 10 + 8 = 18x=10+8=18
14. Solve the equation:
2x+7=192x + 7 = 192x+7=19
Solution:
Subtract 7 from both sides:2x=19−7=122x = 19 – 7 = 122x=19−7=12
Now, divide by 2:x=122=6x = \frac{12}{2} = 6x=212=6
15. Solve the equation:
4x−3=94x – 3 = 94x−3=9
Solution:
Add 3 to both sides:4x=9+3=124x = 9 + 3 = 124x=9+3=12
Now, divide by 4:x=124=3x = \frac{12}{4} = 3x=412=3
16. Solve the equation:
x+34=7\frac{x + 3}{4} = 74x+3=7
Solution:
Multiply both sides by 4:x+3=7×4=28x + 3 = 7 \times 4 = 28x+3=7×4=28
Now, subtract 3 from both sides:x=28−3=25x = 28 – 3 = 25x=28−3=25
17. Solve the equation:
3x+9=273x + 9 = 273x+9=27
Solution:
Subtract 9 from both sides:3x=27−9=183x = 27 – 9 = 183x=27−9=18
Now, divide by 3:x=183=6x = \frac{18}{3} = 6x=318=6
18. Solve the equation:
5×6=10\frac{5x}{6} = 1065x=10
Solution:
Multiply both sides by 6:5x=10×6=605x = 10 \times 6 = 605x=10×6=60
Now, divide by 5:x=605=12x = \frac{60}{5} = 12x=560=12
19. Solve the equation:
x−3=4x – 3 = 4x−3=4
Solution:
Add 3 to both sides:x=4+3=7x = 4 + 3 = 7x=4+3=7
20. Solve the equation:
6x+11=296x + 11 = 296x+11=29
Solution:
Subtract 11 from both sides:6x=29−11=186x = 29 – 11 = 186x=29−11=18
Now, divide by 6:x=186=3x = \frac{18}{6} = 3x=618=3
21. Solve the equation:
7x+2=507x + 2 = 507x+2=50
Solution:
Subtract 2 from both sides:7x=50−2=487x = 50 – 2 = 487x=50−2=48
Now, divide by 7:x=487≈6.857x = \frac{48}{7} \approx 6.857x=748≈6.857
22. Solve the equation:
5x+8=385x + 8 = 385x+8=38
Solution:
Subtract 8 from both sides:5x=38−8=305x = 38 – 8 = 305x=38−8=30
Now, divide by 5:x=305=6x = \frac{30}{5} = 6x=530=6
23. Solve the equation:
x7=9\frac{x}{7} = 97x=9
Solution:
Multiply both sides by 7:x=9×7=63x = 9 \times 7 = 63x=9×7=63
24. Solve the equation:
2(x−3)=142(x – 3) = 142(x−3)=14
Solution:
Expand the left side:2x−6=142x – 6 = 142x−6=14
Add 6 to both sides:2x=14+6=202x = 14 + 6 = 202x=14+6=20
Now, divide by 2:x=202=10x = \frac{20}{2} = 10x=220=10
25. Solve the equation:
3(x+6)=243(x + 6) = 243(x+6)=24
Solution:
Expand the left side:3x+18=243x + 18 = 243x+18=24
Subtract 18 from both sides:3x=24−18=63x = 24 – 18 = 63x=24−18=6
Now, divide by 3:x=63=2x = \frac{6}{3} = 2x=36=2
26. Solve the equation:
5x−2=135x – 2 = 135x−2=13
Solution:
Add 2 to both sides:5x=13+2=155x = 13 + 2 = 155x=13+2=15
Now, divide by 5:x=155=3x = \frac{15}{5} = 3x=515=3
27. Solve the equation:
x+12=25x + 12 = 25x+12=25
Solution:
Subtract 12 from both sides:x=25−12=13x = 25 – 12 = 13x=25−12=13
28. Solve the equation:
3×4=6\frac{3x}{4} = 643x=6
Solution:
Multiply both sides by 4:3x=6×4=243x = 6 \times 4 = 243x=6×4=24
Now, divide by 3:x=243=8x = \frac{24}{3} = 8x=324=8
29. Solve the equation:
x−7=0x – 7 = 0x−7=0
Solution:
Add 7 to both sides:x=0+7=7x = 0 + 7 = 7x=0+7=7
30. Solve the equation:
4x+5=174x + 5 = 174x+5=17
Solution:
Subtract 5 from both sides:4x=17−5=124x = 17 – 5 = 124x=17−5=12
Now, divide by 4:x=124=3x = \frac{12}{4} = 3x=412=3
Simple equations form an essential part of algebra, and practicing different kinds of problems helps strengthen your skills. By breaking down each problem step-by-step, we can easily approach any equation and find the solution. This worksheet covers a variety of equation types, ranging from simple linear equations to word problems.
By solving these problems, you’ll not only improve your understanding of equations but also develop problem-solving techniques that will be useful in future chapters and even higher mathematics.
Also Read: Class 7 Maths – Chapter 4: Simple Equations Solutions
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