1. Solve the inequality 7x + 3 < 2x – 12. Clearly show and explain each step for full credit.?

1) 7x + 3 < 2x - 12

Just collect the like terms, and simplify them to get the answer.

7x - 2x < -12 - 3

5x < -15

x < -3

2) For this question, find the range of x in each inequality. Then, combine them to get the final answer.

First inequality:

3x + 4 > 5

3x > 1

x > 1/3

Second inequality:

x - 2 < 7

x < 9

Combining them, the final answer is 1/3 < x < 9.

3) |4x - 3| = 5

Removing the modulus sign will produce a "±" beside 5. This is because, a number in modulus is

always positive. Therefore, x will have two possible values.

4x - 3 = ±5

4x = 5+3 or -5+3

= 8 or -2

x = 2 or -1/2.

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