Question

Solve -7 < 3x + 2 < 14

Answer 1

Answer:

$- 7 < (3x + 2) < 14 \\ \\ = \: \: - 7 - 2 < 3x < 14 - 2 \\ \\ = \: \: - 9 < 3x < 12 \\ \\ = \: \: \frac{ - 9}{3} < \frac{3x}{3} < \frac{12}{3} \\ \\ = { \boxed{ \boxed{ - 3 < x < 4}}}$

Answer 2

Answer:

-3<x<4

Step-by-step explanation:

Hi there!

We are given the double inequality -7<3x+2<14 and we want to solve it.

If we have a double inequality and we want to do something (like subtract 3), then we must subtract 3 from the left side, middle, and right side.

An example would be with the inequality 1<x+3<5

In order to isolate x, we'll subtract 3 from the center. However, we'll also be needing to subtract 3 from the left (1-3) and the right (5-3)

Hence,

1<x+3<5

-3   -3  -3

___________

-2<x<2

In our problem then, we'll be subtracting 2 from EVERY side.

-7<3x+2<14

-2      -2   -2

________________

-9 < 3x  < 12

Now in order to isolate x, we'll divide by 3, which once again, we divide on EVERY side

-3<x<4

Hope this helps!