# Practice Test on Linear Equations

In math equations, students can practice test on linear equations in one variable showing step-by-step solution using addition, subtraction, multiplication and division. While practicing this sheet keep in mind the basic concept on linear equations.

Notes to practice test on linear equations:

An equation which involves only one variable whose highest power is 1 is known as linear equation in that variable.

We can add or subtract the same number to both sides of the equation.

We can divide or multiply both sides of the equation by the same non-zero integer.

Transposition is a process in which any term in an equation can be shifted to the other side of equal to sign by simply changing the sign from
(+ to -)(- to +)(× to ÷), and (÷ to ×).

The process of multiplying the numerator on L.H.S. with denominator on R.H.S. and multiplying denominator on L.H.S. with numerator on R.H.S. is called cross multiplication.

Solve the following equations:

(a) 5x - 11 = 3x + 9

(b) 3y + 4 = 7 - 2y

(c) 9 - 2(x - 5) = x + 10

(d) 5(y - 1) = 3(2y - 5) - (1 - 3y)

(e) 2(x - 1) - 6x = 10 - 2(x - 4)

(f) x/3 - (x - 2)/2 = 7/3

(g) (x - 3)/4 + (x - 1)/5 - (x - 2)/3 = 1

(h) (3y - 2)/3 + (2y + 3)/3 = (y + 7)/6

(i) (8x - 5)/(7x + 1) = -4/5

(j) (5 - 7x)/(2 + 4x) = -8/7

(k) (x - 2)/(x - 3) = (x - 1)/(x + 1)

(l) (2x - 5)/(3x - 1) = (2x - 1)/(3x + 2)

(m) (3 - 7x)/(15 + 2x) = 0

(n) (0.4y - 3)/(1.5y + 9) = -7/5

(o) 2/(3x - 1) + 3/(3x + 1) = 5/3x

(p) 2/(x - 3) + 1/(x - 1) = 5/(x - 1) - 2/(x - 2)

(q) 15(x - y) - 3(x - 9) + 5(x + 6) = 0

(r) y/2 - 1/2 = y/3 + 1/4

(s) (0.5y - 9)/0.25 = 4y - 3

(t) [17(2 - y) - 5(y + 12)]/(1 - 7y) = 8

Answers for the practice test on linear equations in one variable are given below to check the exact answers of the equations.

(a) 10

(b) 3/5

(c) 3

(d) 11/4

(e) -10

(f) -8

(g) 11

(h) 5/9

(i) 21/68

(j) 3

(k) 5/3

(l) -11/6

(m) 3/7

(n) - 96/25

(o) 5/3

(p) 7/3

(q) -1/6

(r) 9/2

(s) -16.5

(t) 1

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