Answer:
The appropriate response is x ≤ [tex]\frac{17}{2}[/tex] ⇒ A
Step-by-step explanation:
The inequality is [tex]\frac{2x+7}{-4}[/tex] ≥ - 6
To solve the inequality at first multiply both sides of the inequality by -4, but remember when you multiply the sides of the inequality by negative number you must reverse the sign of the inequality
( -2 > -3 if you multiply both sides by -1, then the answer must be 2 < 3)
∵ [tex]\frac{2x+7}{-4}[/tex] ≥ - 6
- Multiply both sides by -4
∴ [tex]-4(\frac{2x+7}{-4})[/tex] ≤ - 4(- 6)
- Cancel -4 up with -4 down in the left hand side
∴ 2x + 7 ≤ 24
- Subtract 7 from both sides
∴ 2x ≤ 17
- Divide both sides by 2
∴ x ≤ [tex]\frac{17}{2}[/tex]
∴ The appropriate response is x ≤ [tex]\frac{17}{2}[/tex]
