Question

solve for ( x ) and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (( varnothing )), leave the number line blank. (-5 geq -5x + 10) and (-5x + 10 > -50)

Explanation:

Step1: Solve first inequality

Start with $-5 \geq -5x + 10$.
Subtract 10 from both sides:
$-5 - 10 \geq -5x$
$-15 \geq -5x$
Divide by -5 (reverse inequality):
$3 \leq x$ or $x \geq 3$

Step2: Solve second inequality

Start with $-5x + 10 > -50$.
Subtract 10 from both sides:
$-5x > -50 - 10$
$-5x > -60$
Divide by -5 (reverse inequality):
$x < 12$

Step3: Combine inequalities

Find overlap of $x \geq 3$ and $x < 12$

Answer:

$3 \leq x < 12$

Number Line Graph Instructions:

1. Draw a closed circle at $x=3$ (since the inequality includes equality)
2. Draw an open circle at $x=12$ (since the inequality does not include equality)
3. Shade the region between the two circles.