Question

match each compound inequality on the left to the graph that represents its solution on the right. 8x < 24 and -8 ≤ 2x - 4 5x - 2 > 13 or -4x ≥ 8 -25 ≤ 9x + 2 < 20 clear click and hold on an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video. question id: 559136

Explanation:

Step1: Solve $8x < 24$ and $-8\leq2x - 4$

For $8x < 24$, divide both sides by 8: $x < 3$. For $-8\leq2x - 4$, add 4 to both sides: $-4\leq2x$, then divide by 2: $-2\leq x$. So the solution is $-2\leq x < 3$.

Step2: Solve $5x - 2>13$ or $-4x\geq8$

For $5x - 2>13$, add 2 to both sides: $5x>15$, divide by 5: $x > 3$. For $-4x\geq8$, divide by - 4 and reverse the inequality sign: $x\leq - 2$. So the solution is $x\leq - 2$ or $x > 3$.

Step3: Solve $-25\leq9x + 2<20$

Subtract 2 from all parts: $-27\leq9x<18$. Divide all parts by 9: $-3\leq x < 2$.

Answer:

1. $8x < 24$ and $-8\leq2x - 4$ matches the graph with a closed - circle at $x=-2$ and an open - circle at $x = 3$.
2. $5x - 2>13$ or $-4x\geq8$ matches the graph with a closed - circle at $x=-2$ and an open - circle at $x = 3$ where the non - overlapping parts are shaded.
3. $-25\leq9x + 2<20$ matches the graph with a closed - circle at $x=-3$ and an open - circle at $x = 2$.