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.

-3x + 4 ≤ -23 and -29 ≥ -3x + 4

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: $-3x + 4 - 4 \leq -23 - 4$ → $-3x \leq -27$
Divide by -3 (reverse inequality): $x \geq 9$

Step2: Solve second inequality

Subtract 4 from both sides: $-29 - 4 \geq -3x + 4 - 4$ → $-33 \geq -3x$
Divide by -3 (reverse inequality): $11 \leq x$ → $x \geq 11$

Step3: Find intersection

The solution to "and" is the overlap of $x \geq 9$ and $x \geq 11$, which is $x \geq 11$.

Answer:

Inequality Notation: $x \geq 11$
Number Line: Plot a closed circle at 11 and shade to the right.