Question

match each compound inequality on the left to the graph that represents its solution on the right.
-5x + 9 < - 6 or -3x + 1 ≥ 7
-6x > - 18 and 1 ≤ 2x + 5
-16 ≤ 6x + 2 < 14
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

Solve $-5x + 9 < - 6$:
Subtract 9 from both sides: $-5x<-6 - 9=-15$.
Divide both sides by - 5 and reverse the inequality sign: $x > 3$.
Solve $-3x + 1\geq7$:
Subtract 1 from both sides: $-3x\geq7 - 1 = 6$.
Divide both sides by - 3 and reverse the inequality sign: $x\leq - 2$.
The solution of $-5x + 9 < - 6$ or $-3x + 1\geq7$ is $x\leq - 2$ or $x > 3$.

Step2: Solve the second compound - inequality

Solve $-6x>-18$:
Divide both sides by - 6 and reverse the inequality sign: $x < 3$.
Solve $1\leq2x + 5$:
Subtract 5 from both sides: $1-5\leq2x$, i.e., $-4\leq2x$.
Divide both sides by 2: $-2\leq x$.
The solution of $-6x > - 18$ and $1\leq2x + 5$ is $-2\leq x<3$.

Step3: Solve the third compound - inequality

Solve $-16\leq6x + 2$:
Subtract 2 from both sides: $-16 - 2\leq6x$, i.e., $-18\leq6x$.
Divide both sides by 6: $-3\leq x$.
Solve $6x + 2<14$:
Subtract 2 from both sides: $6x<14 - 2 = 12$.
Divide both sides by 6: $x < 2$.
The solution of $-16\leq6x + 2<14$ is $-3\leq x<2$.

Answer:

$-5x + 9 < - 6$ or $-3x + 1\geq7$ matches the graph with a closed - circle at $x=-2$ and an open - circle at $x = 3$.
$-6x > - 18$ and $1\leq2x + 5$ matches the graph with a closed - circle at $x=-2$ and an open - circle at $x = 3$.
$-16\leq6x + 2<14$ matches the graph with a closed - circle at $x=-3$ and an open - circle at $x = 2$.