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 (∅), leave the number line blank.

$-5x + 4 \geq -21$ and $-5x + 4 > -56$

answer attempt 1 out of 2

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12; instruction: touch and drag to plot line.
submit answer

Explanation:

Step1: Solve first inequality

Subtract 4 from both sides: $-5x + 4 - 4 \geq -21 - 4$ → $-5x \geq -25$.
Divide by -5 (reverse inequality): $x \leq 5$.

Step2: Solve second inequality

Subtract 4 from both sides: $-5x + 4 - 4 > -56 - 4$ → $-5x > -60$.
Divide by -5 (reverse inequality): $x < 12$.

Step3: Find intersection

The solution to "and" is the overlap of $x \leq 5$ and $x < 12$, which is $x \leq 5$.

Answer:

Inequality Notation: $x \leq 5$
Number Line: Plot a closed circle at 5 and shade to the left.