Easy Algebra Step-by-Step

Solving Linear Equations and Inequalities 155

Tools for Solving Linear Equations

Add the same number to both sides.

Subtract the same number from both sides.

Multiply both sides by the same nonzero

number.

Divide both sides by the same nonzero number.

Problem Solve the equation.

a. 5 x+ 9 = 3 x − 1

b. 4(x − 6) = 40

c. −3x − 7 = 14

d. 3 x − 2 = 7 − 2x

e.

xx

=

3

2

24 x+

5

Solution

a. 5 x+ 9 = 3 x − 1

Step 1. The variable appears on both sides of the equation, so subtract 3x

from the right side to remove it from that side. To maintain balance,

subtract 3x from the left side, too.

5 x+ 9 − 3 x= 3 x − 1 − 3 x

Step 2. Simplify both sides by combining like variable terms.

2 x + 9 = −1

Step 3. 9 is added to the variable term, so subtract 9 from both sides.

2 x+ 9 − 9 = −1 − 9

Step 4. Simplify both sides by combining constant terms.

2 x = − 10

Step 5. You want the coeffi cient of x to be 1, so divide both sides by 2.

21 x 0

2 2

=

Step 6. Simplify.

x= − 5

P It is important to remember

that when you are solving an

equation, you must never multiply

or divide both sides by 0.