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Worksheet on Linear Equations

Practice worksheet on linear equations in one variable. Students can recall the lesson and practice the equations step-by-step and then try to represent the solution of the linear equation graphically.

1. Solve each of the following equations and represent the solution graphically.

(a) 7x + 2 = -19

(b) 3x - 1/3 = 5

(d) -7x = 21

(e) 18 - 7x = -3

(f) 3(x + 4) = 21

(g) 2x/3 - 3x/5 = 8

(h) 3x - 9 = 5x - 3

(i) 3(x - 3) = 4(2x + 1)

2. Solve each of the following equations and check your solution by substituting in the equation.

(a) 3x/2 - 10 = 1/2

(b) x/2 - x/3 = 8

(d) 2(x - 2) - 5(x - 5) = 4(x - 8) - 2(x - 2)

(e) (2 - y)/(y + 7) = 3/5

(f) (3x + 2)/(2x - 3) = - 3/2

(g) (x - 8 )/3 = (x - 3)/5

(h) 0.25(4y - 3) = 0.5y - 9

3. Solve the following equations and check your answer:

(i) m - 7 = 1

(ii) y + 7 = 5

(ⅲ) $\frac{x}{7}$ + 3 = 5

(iv) 2x + 22 = 48

(v) 11k - 5 = 50

(vi) 2p - 10 = - 14

4. For what value of a will the following statements be true?:

(i) 7x + 5 = 26

(ii) 2m - 4 = 18

(iii) z - 9 = - 9

(iv) d - 100 = - 126

(v) k + 8 = 15

(vi) h - 2 = 13

5. Solve the following equations:

(i) p + 8.6 = 26

(ii) z - 2$\frac{3}{4}$ = 6$\frac{1}{4}$

6. Frame the equations and solve them:

(i) If one-fifth of a number is increased by 6, the sum will be 25.

(ii) If y is multiplied by 12, the result is 108.

$Find the Length of a Rectangle$

7. Find the length of a rectangle as shown in the adjoining figure, if its perimeter is 250 metres and breadth is 35 metres.

8. Multiple choice Questions:

(i) Solving the equation 2m - 16 = 5 - m we get

(a) m = 2

(b) m = 4

(d) m = 9

(ii) The solution of the linear equation is k/3 - k/4 = 12

(a) k = 136

(b) k = 120

(d) k= 144

(iii) On solving 7p + 4 = 4(p + 4) the value of p obtained is

(a) 4

(b) -8

(d) -12

9. Solve the following equations and check the results:

(i) 3(4z + 2) - 6 = 2(9 - 3z)

(ii) p - 3$\frac{1}{2}$ = 1$\frac{1}{2}$

(iii) $\frac{k}{3}$ + 9.1 = 1.1

10. If a number increased by 23 is equal to 87, find the number.

11. If 13 less than twice a number is 37, what is the number?

12. Solve the following equations and check your answer:

(i) k - 3 = 2

(ii) p + 7 = 5

(iii) $\frac{z}{7}$ + 5 = 7

(iv) 2m + 22 = 44

(v) 8n - 6 = 10

13. Nairitee buys some erasers, each costing ₹ 5, for ₹ 60. Find the number of erasers she bought.

Answers for the worksheet on linear equations in one variable are given below so that students can check the exact answers after solving the equations.