Question

1. drag each inequality to the graph of its solution. 7x + 8 < 29 2x - 1 > 5 32 - x ≥ 29 33 - 8x ≤ 9

Explanation:

Step1: Solve $7x + 8<29$

Subtract 8 from both sides: $7x<29 - 8$, so $7x<21$. Then divide both sides by 7: $x < 3$.

Step2: Solve $2x-1>5$

Add 1 to both sides: $2x>5 + 1$, so $2x>6$. Then divide both sides by 2: $x>3$.

Step3: Solve $32 - x\geq29$

Subtract 32 from both sides: $-x\geq29 - 32$, so $-x\geq - 3$. Multiply both sides by - 1 and reverse the inequality sign: $x\leq3$.

Step4: Solve $33-8x\leq9$

Subtract 33 from both sides: $-8x\leq9 - 33$, so $-8x\leq - 24$. Divide both sides by - 8 and reverse the inequality sign: $x\geq3$.

• For $x < 3$, it corresponds to the number - line with an open - circle at 3 and shading to the left.
• For $x>3$, it corresponds to the number - line with an open - circle at 3 and shading to the right.
• For $x\leq3$, it corresponds to the number - line with a closed - circle at 3 and shading to the left.
• For $x\geq3$, it corresponds to the number - line with a closed - circle at 3 and shading to the right.

Answer:

$7x + 8<29$ to the number - line with an open - circle at 3 and shading to the left.
$2x - 1>5$ to the number - line with an open - circle at 3 and shading to the right.
$32 - x\geq29$ to the number - line with a closed - circle at 3 and shading to the left.
$33 - 8x\leq9$ to the number - line with a closed - circle at 3 and shading to the right.