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
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 the target before releasing. the target will highlight or the cursor will change. need help? watch this video.
clear

Explanation:

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

For $4x - 3>9$, add 3 to both sides:
$4x-3 + 3>9 + 3$, so $4x>12$, then divide both sides by 4, we get $x > 3$.
For $-8x\geq16$, divide both sides by - 8. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $x\leq - 2$. The solution of this compound - inequality 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, we get $x\geq - 3$.
For $10>2x + 6$, subtract 6 from both sides: $10-6>2x+6 - 6$, so $4>2x$. Then divide both sides by 2, we get $x < 2$. The solution of this compound - inequality is $-3\leq x<2$.

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

Subtract 2 from all parts of the compound - inequality: $-10-2\leq6x + 2-2<20-2$, so $-12\leq6x<18$. Then divide all parts by 6: $\frac{-12}{6}\leq\frac{6x}{6}<\frac{18}{6}$, we get $-2\leq x<3$.

Answer:

Match $4x - 3>9$ or $-8x\geq16$ with the graph that has 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 that has a closed circle at - 3 and an open circle at 2 and shading in between.
Match $-10\leq6x + 2<20$ with the graph that has a closed circle at - 2 and an open circle at 3 and shading in between.