Easy Algebra Step-by-Step

160 Easy Algebra Step-by-Step

have a true inequality, namely, −8 < −2. You can verify that −8 < −2 is a true

inequality by observing that −2 is to the right of −8 on the number line as

shown in Figure 14.2.

If you neglect to reverse the direction of the inequality symbol after mul-

tiplying both sides of 8 > 2 by −1, you get the false inequality −8 > −2.

Problem Solve the inequality.

a. 5 x + 6 < 3 x − 2

b. 4(x − 6) ≥ 44

c. −3x − 7 > 14

Solution

a. 5 x + 6 < 3 x − 2

Step 1. The variable appears on both sides of the inequality, 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 + 6 − 3 x < 3 x − 2 − 3 x

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

2 x + 6 < −2

Step 3. 6 is added to the variable term, so sub-

tract 6 from both sides.

2 x + 6 − 6 < −2 − 6

Step 4. Simplify both sides by combining constant terms.

2 x < − 8

When solving an inequality, do

not reverse the direction of the

inequality symbol because of

subtracting the same number

from both sides.

Figure 14.1 The numbers 2 and 8 on the number line

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

Figure 14.2 The numbers −8 and −2 on the number line