Question

Solve the inequality
|0.2x+6| <0.15

Answer 1

To solve the inequality |0.2x+6| < 0.15, we split it into two separate inequalities and find that the solution for x is -30.75 < x < -29.25.

Step-by-step explanation:

To solve the inequality |0.2x+6| < 0.15, we first consider the absolute value function. This means we are looking for values of x that make 0.2x + 6 less than 0.15 and greater than -0.15. We split this into two separate inequalities:

1. 0.2x + 6 < 0.15
2. 0.2x + 6 > -0.15

Solving the first inequality for x:

0.2x < 0.15 - 6
0.2x < -5.85
x < -5.85 / 0.2
x < -29.25

Solving the second inequality for x:

0.2x > -0.15 - 6
0.2x > -6.15
x > -6.15 / 0.2
x > -30.75

Therefore, combining the two inequalities, we find the solution for x is:

-30.75 < x < -29.25.

Answer 2

- 30.75 < x < - 29.25

Step-by-step explanation:

Inequalities of the type | x | < a , always have solutions of the form

- a < x < a

Given

| 0.2x + 6 | < 0.15, then

- 0.15 < 0.2x + 6 < 0.15 ( subtract 6 from all 3 intervals )

- 6.15 < 0.2x < - 5.85 ( divide all intervals by 0.2 )

- 30.75 < x < - 29.25