Question

I have 100 points i need some help!!

Answer 1

Answer:

Option D:  $\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}$

Step-by-step explanation:

GIven the following inequality statement:

$\displaystyle\mathsf{7x\:+\:6\:\geq \:\frac{-x}{2}}$

Start by eliminating the fraction on the right-hand side.

Multiply both sides of the inequality statement by 2:

$\displaystyle\mathsf{2(7x\:+\:6)\:\geq \:\bigg[\frac{-x}{2}\bigg](2)}$

2(7x + 6) ≥ -x

Next, distribute 2 into the terms inside the parenthesis:

14x + 12 ≥ -x

Subtract 12 from both sides:

14x + 12 - 12 ≥ -x - 12

14x  ≥ -x - 12

Add x to both sides:

14x + x  ≥ -x + x - 12

15x ≥ - 12

Divide both sides by 15 to isolate x:

$\displaystyle\mathsf{\frac{15x}{15}\:=\:\frac{-12}{15}}$

$\displaystyle\mathsf{x\geq -\frac{4}{5}}$ or  $\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}$

Therefore, the correct answer is Option D:  $\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}$