Easy Algebra Step-by-Step

Solving Linear Equations and Inequalities 157

Step 4. Simplify.

x= − 7

Step 5. Check your answer by substituting −7 for x in the original equation,

−3x − 7 = 14.

Substitute −7 for x on the left side of the equation: −3x − 7 = −3(−7) −

7 = 21 − 7 = 14. On the right side, you have 14 as well. Both sides

equal 14, so −7 is the correct answer.

d. 3 x − 2 = 7 − 2x

Step 1. The variable appears on both sides of the equation, so add 2x to the

right side to remove it from that side. To maintain balance, add 2x to

the left side, too.

3 x − 2 + 2 x = 7 − 2x + 2 x

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

5 x − 2 = 7

Step 3. 2 is subtracted from the variable term, so add 2 to both sides.

5 x − 2 + 2 = 7 + 2

Step 4. Simplify both sides by combining constant terms.

5 x= 9

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

59 x

55

=

Step 6. Simplify.

x = 1.8

Step 7. Check your answer by substituting 1.8 for x in the original equation,

3 x − 2 = 7 − 2x.

Substitute 1.8 for x on the left side of the equation: 3x − 2 = 3(1.8) −

2 = 5.4 − 2 = 3.4. Similarly, on the right side, you have 7 − 2x=

7 − 2(1.8) = 7 −3.6 = 3.4. Both sides equal 3.4, so 1.8 is the correct

answer.