Answer:
[tex] - 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}}}[/tex]
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!
