which interval notation would go with this equation

-5(4x - 14) ≥ -25x + 35

A) {x|x < -7}; (-∞, -7)

B) {x|x ≤ -7}; (-∞, -7]

C) {x|x > -7}; (-7, ∞)

D) {x|x ≥ -7}; [-7, ∞)

- 5 ( 4 x - 14 ) ¡Ý - 25 x + 35

- 20 x + 70 ¡Ý - 25 x + 35

- 20 x + 25 x ¡Ý 35 - 70

5 x ¡Ý - 35 Divide both sides by 5

x ¡Ý - 7

Ansver D

¡Ý mean greater or equal

To determine the interval notation that goes with the given equation, let's solve the inequality step by step:

-5(4x - 14) ≥ -25x + 35

First, distribute -5 to the terms inside the parentheses:

-20x + 70 ≥ -25x + 35

Next, move the variables to one side and the constants to the other side by adding 25x to both sides:

5x + 70 ≥ 35

Subtract 70 from both sides:

5x ≥ -35

Finally, divide both sides by 5 to solve for x:

x ≥ -7

The solution to the inequality is x ≥ -7.

Now, let's match this solution with the given interval notations:

A) {x|x < -7}; (-∞, -7)

Since the solution is x ≥ -7, this option is incorrect because it states x < -7.

B) {x|x ≤ -7}; (-∞, -7]

Since the solution is x ≥ -7, this option is incorrect because it states x ≤ -7.

C) {x|x > -7}; (-7, ∞)

Since the solution is x ≥ -7, this option is incorrect because it states x > -7.

D) {x|x ≥ -7}; [-7, ∞)

Since the solution is x ≥ -7, this option is correct because it states x ≥ -7 and the interval notation matches the solution.

Therefore, the correct interval notation that goes with the given equation is option D) {x|x ≥ -7}; [-7, ∞).