Question

11 match each number line to its inequality. -5x + 13 ≥ 29 -10x + 5 + 7x ≥ 17 4x + 8 + (-5x) ≤ 18

Explanation:

Step1: Solve the first - inequality

Solve $-5x + 13\geq29$. Subtract 13 from both sides: $-5x\geq29 - 13$, so $-5x\geq16$. Divide both sides by - 5 and reverse the inequality sign (since dividing by a negative number), we get $x\leq-\frac{16}{5}=-3.2$.

Step2: Solve the second - inequality

Solve $-10x + 5+7x\geq17$. Combine like - terms: $-3x+5\geq17$. Subtract 5 from both sides: $-3x\geq17 - 5$, so $-3x\geq12$. Divide both sides by - 3 and reverse the inequality sign, we get $x\leq - 4$.

Step3: Solve the third - inequality

Solve $4x + 8+( - 5x)\leq18$. Combine like - terms: $4x-5x + 8\leq18$, so $-x+8\leq18$. Subtract 8 from both sides: $-x\leq18 - 8$, so $-x\leq10$. Multiply both sides by - 1 and reverse the inequality sign, we get $x\geq - 10$.

For the number line with a closed - circle at $x = - 4$ and the arrow pointing to the left, it matches $-10x + 5+7x\geq17$.
For the number line with a closed - circle at $x=-10$ and the arrow pointing to the right, it matches $4x + 8+( - 5x)\leq18$.
For the number line with a closed - circle at $x=-3.2$ and the arrow pointing to the left, it matches $-5x + 13\geq29$.

Answer:

First number line (closed - circle at $x = - 4$, arrow left): $-10x + 5+7x\geq17$
Second number line (closed - circle at $x=-10$, arrow right): $4x + 8+( - 5x)\leq18$
Third number line (closed - circle at $x=-3.2$, arrow left): $-5x + 13\geq29$