Question

Question is in picture below

Answer 1

C

Explanation:

`-12<4x \leq 8 \\ \\ -3<x \leq 2`

Answer 2

[C] x > -3 and x ≤ 2

Explanation:

`\mathrm{Given:}-9 < 4x+3\leq 11`

`\mathrm{{If}\:a < u\le \:b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u\le \:b}`

`-9 < 4x+3\quad \mathrm{and}\quad \:4x+3\le \:11`

`\mathrm{solving\;the\;first\;one}:-9 < 4x+3`

`\mathrm{Switch\:sides}`

`4x+3 > -9`

`\mathrm{subtract\;3\;from\;both\;sides}:\\4x > -12`

`\mathrm{Divide\:both\:sides\:by\:}4\\\\(4x)/(4) > (-12)/(4)`

`x > -3`

`\mathrm{Now\;with\;the\;second\;one}:4x+3\le \:11`

`\mathrm{subtract\;3\;from\;both\;sides}:\\4x\le \:8`

`\mathrm{Divide\:both\:sides\:by\:}4`

`(4x)/(4)\le (8)/(4)`

`x\le \:2`

Therefore, the answer is [C] x > -3 and x ≤ 2

RevyBreeze~