Question

graph the solution set of the compound inequality $4(3 - x) < -2$ and $\frac{x - 1}{4} leq -1$. choose the correct graph below.
a.
<---(-10)----0----10--->
b.
<---(-10)----(----0--------10--->
c.
<---(-10)--------0----)----10--->
d.
<---(-10)--------0----(----10--->
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is
b. the solution is the empty set.

Explanation:

Step1: Solve first inequality

Start with $4(3 - x) < -2$.
Divide both sides by 4:
$\frac{4(3 - x)}{4} < \frac{-2}{4}$
Simplify: $3 - x < -\frac{1}{2}$
Subtract 3 from both sides:
$-x < -\frac{1}{2} - 3$
$-x < -\frac{7}{2}$
Multiply by -1 (reverse inequality):
$x > \frac{7}{2}$ or $x > 3.5$

Step2: Solve second inequality

Start with $\frac{x - 1}{4} \leq -1$.
Multiply both sides by 4:
$x - 1 \leq -4$
Add 1 to both sides:
$x \leq -3$

Step3: Find intersection of solutions

The compound inequality uses "and", so we need values of $x$ that satisfy both $x > 3.5$ and $x \leq -3$. There are no such values.

Answer:

Graph Choice:

A. (the empty number line)

Interval Notation Choice:

B. The solution is the empty set.