Question

} { -4 \geq -6 }" alt="\frac{2x + 7} { -4 \geq -6 }" align="absmiddle" class="latex-formula">
Select the appropriate response
A)X ≤ 17/2
B)X ≤ 19/2
C)X ≤ 17/0
D)X ≤ 17/x

Answer 1

Answer:

The appropriate response is x ≤ $\frac{17}{2}$ ⇒ A

Step-by-step explanation:

The inequality is $\frac{2x+7}{-4}$ ≥ - 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)

∵  $\frac{2x+7}{-4}$ ≥ - 6

- Multiply both sides by -4

∴  $-4(\frac{2x+7}{-4})$ ≤ - 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 ≤ $\frac{17}{2}$

∴ The appropriate response is x ≤ $\frac{17}{2}$