Question

match each compound inequality on the left to the graph that represents its solution on the right.
4x - 3 > 9 or -8x ≥ 16
8x ≥ - 24 and 10 > 2x + 6
-10 ≤ 6x + 2 < 20
clear
click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over target before releasing. the target will highlight or the cursor will change. need help? watch this video.

Explanation:

Step1: Solve the first compound - inequality $4x - 3>9$ or $-8x\geq16$

For $4x - 3>9$, add 3 to both sides: $4x>9 + 3$, so $4x>12$, then divide by 4, $x > 3$. For $-8x\geq16$, divide both sides by - 8 and reverse the inequality sign, $x\leq - 2$. The solution is $x>3$ or $x\leq - 2$.

Step2: Solve the second compound - inequality $8x\geq - 24$ and $10>2x + 6$

For $8x\geq - 24$, divide both sides by 8, $x\geq - 3$. For $10>2x + 6$, subtract 6 from both sides: $4>2x$, then divide by 2, $x < 2$. The solution is $-3\leq x<2$.

Step3: Solve the third compound - inequality $-10\leq6x + 2<20$

Subtract 2 from all parts: $-10-2\leq6x+2 - 2<20 - 2$, so $-12\leq6x<18$. Divide all parts by 6: $-2\leq x<3$.

Match the solutions to the graphs:

• The graph for $x>3$ or $x\leq - 2$ is the one with an open - circle at 3 and shading to the right and a closed - circle at - 2 and shading to the left.
• The graph for $-3\leq x<2$ is the one with a closed - circle at - 3 and an open - circle at 2.
• The graph for $-2\leq x<3$ is the one with a closed - circle at - 2 and an open - circle at 3.

Answer:

Match $4x - 3>9$ or $-8x\geq16$ with the graph having an open - circle at 3 and shading to the right and a closed - circle at - 2 and shading to the left.
Match $8x\geq - 24$ and $10>2x + 6$ with the graph having a closed - circle at - 3 and an open - circle at 2.
Match $-10\leq6x + 2<20$ with the graph having a closed - circle at - 2 and an open - circle at 3.