Question

solve for $x$ and graph the solution on the number line below.$4x + 8 \geq -32$ and $48 > 4x + 8$answer attempt 1 out of 2$<$ $>$ $leq$ $geq$ orinequality notation:number line:click and drag to plot line.

Explanation:

Step1: Solve first inequality

$4x + 8 \geq -32$
Subtract 8 from both sides:
$4x \geq -32 - 8$
$4x \geq -40$
Divide by 4:
$x \geq -10$

Step2: Solve second inequality

$48 > 4x + 8$
Subtract 8 from both sides:
$48 - 8 > 4x$
$40 > 4x$
Divide by 4:
$10 > x$ or $x < 10$

Step3: Combine the solutions

Since it's an "and" compound inequality, we take the overlap of $x \geq -10$ and $x < 10$, resulting in $-10 \leq x < 10$.

Step4: Graph instructions

On the number line:

• Place a closed circle at $-10$ (since the inequality includes equality)
• Place an open circle at $10$ (since the inequality does not include equality)
• Draw a solid line connecting the two circles to represent all values between them.

Answer:

$-10 \leq x < 10$