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, ∞).