Easy Algebra Step-by-Step

Solving Linear Equations and Inequalities 161

When solving an inequality, do not

reverse the direction of the inequality

symbol because of dividing both sides

by a positive number.

Step 5. You want the coeffi cient of x to be 1,

so divide both sides by 2.

2 x 8

22

<

−

Step 6. Simplify.

x < −4 is the answer.

b. 4(x − 6) ≥ 44

Step 1. Use the distributive property to remove parentheses.

4 x − 24 ≥ 44

Step 2. 24 is subtracted from the variable term,

so add 24 to both sides.

4 x − 24 + 24 ≥ 44 + 24

Step 3. Simplify both sides by combining constant terms.

4 x ≥ 68

Step 4. You want the coeffi cient of x to be 1, so divide both sides by 4.

46 x 8

44

≥

Step 5. Simplify.

x≥ 17 is the answer.

c. − 37 x− > 14

Step 1. 7 is subtracted from the variable term, so add 7 to both sides.

−3x − 7 + 7 > 14 + 7

Step 2. Simplify both sides by combining constant terms.

− 3 x> 21

Step 3. You want the coeffi cient of x to be 1, so divide both sides by −3

and reverse the direction of the inequal-

ity because you divided by a negative

number.

−

−

<

32 x 1

33 −

When solving an inequality, do

not reverse the direction of the

inequality because of adding the

same number to both sides.

When solving an inequality,

remember to reverse the direction

of the inequality when you divide

both sides by the same negative

number.