Question

record your matches in the table.
$10 + 5xleq - 10$
$-x + 11geq6$
$9<-\frac{x}{3}+7$
$\frac{1}{2}x - 5<-7$
$11>-1 - 2x$
$-4 + 0.2xgeq - 3$
graph
inequality

Explanation:

Step1: Solve $10 + 5x\leq - 10$

Subtract 10 from both sides: $5x\leq - 10 - 10$, so $5x\leq - 20$. Then divide both sides by 5, we get $x\leq - 4$.

Step2: Solve $-x + 11\geq6$

Subtract 11 from both sides: $-x\geq6 - 11$, so $-x\geq - 5$. Multiply both sides by - 1 (reverse the inequality sign), we have $x\leq5$.

Step3: Solve $9<-\frac{x}{3}+7$

Subtract 7 from both sides: $9 - 7<-\frac{x}{3}$, so $2<-\frac{x}{3}$. Multiply both sides by - 3 (reverse the inequality sign), we get $x<-6$.

Step4: Solve $\frac{1}{2}x - 5<-7$

Add 5 to both sides: $\frac{1}{2}x<-7 + 5$, so $\frac{1}{2}x<-2$. Multiply both sides by 2, we have $x<-4$.

Step5: Solve $11>-1 - 2x$

Add 1 to both sides: $11 + 1>-2x$, so $12>-2x$. Divide both sides by - 2 (reverse the inequality sign), we get $x>-6$.

Step6: Solve $-4+0.2x\geq - 3$

Add 4 to both sides: $0.2x\geq - 3 + 4$, so $0.2x\geq1$. Divide both sides by 0.2, we have $x\geq5$.

Match the solutions with the graphs:

• For $x\leq - 4$, it matches the graph with a closed - circle at - 4 and shading to the left.
• For $x\leq5$, it matches the graph with a closed - circle at 5 and shading to the left.
• For $x<-6$, it matches the graph with an open - circle at - 6 and shading to the left.
• For $x<-4$, it matches the graph with an open - circle at - 4 and shading to the left.
• For $x>-6$, it matches the graph with an open - circle at - 6 and shading to the right.
• For $x\geq5$, it matches the graph with a closed - circle at 5 and shading to the right.

Answer:

Match the inequalities with the graphs as follows:
$10 + 5x\leq - 10$ with the graph having a closed - circle at - 4 and shading to the left.
$-x + 11\geq6$ with the graph having a closed - circle at 5 and shading to the left.
$9<-\frac{x}{3}+7$ with the graph having an open - circle at - 6 and shading to the left.
$\frac{1}{2}x - 5<-7$ with the graph having an open - circle at - 4 and shading to the left.
$11>-1 - 2x$ with the graph having an open - circle at - 6 and shading to the right.
$-4 + 0.2x\geq - 3$ with the graph having a closed - circle at 5 and shading to the right.