select the correct answer. which graph represents the solution to this inequality? $-\frac{1}{4}(12x + 8)…
select the correct answer. which graph represents the solution to this inequality? $-\frac{1}{4}(12x + 8) leq - 2x + 11$
Answer
Explanation:
Step1: Expand the left - hand side
[ \begin{align*} -\frac{1}{4}(12x + 8)&=-3x-2 \end{align*} ] So the inequality becomes $-3x - 2\leq - 2x+11$.
Step2: Add $3x$ to both sides
[ \begin{align*} -3x - 2+3x&\leq - 2x+11+3x\ -2&\leq x + 11 \end{align*} ]
Step3: Subtract 11 from both sides
[ \begin{align*} -2-11&\leq x+11 - 11\ -13&\leq x \end{align*} ] This means $x\geq - 13$. The graph of $x\geq - 13$ has a closed - circle at $x = - 13$ and the line extends to the right.
Answer:
C.