Solve |9 – 4x| > 7 and write interval notation for the solution set.
A.(1/2, 4)
B. (-4,-1/2)
C. (1/2, infinity)
D. (-infinity U (4, infinity)
I say the answer is D..Am i correct?
Undo the absolute value by considering the two possible solutions:
9 - 4x > 7
and 9 - 4x < -7
Solve each separately:
9 - 4x > 7
-4x > -2
x < 1/2
9 - 4x < -7
-4x < -16
x > 4
The answer should be (-infinity, 1/2) U (4, infinity).
You appear to have left off the 1/2 in copying answer D. However, it appears to be answer D.
Yes i left off the 1/2 by mistake, but D is the answer like i said? Thanks!
To solve the inequality |9 – 4x| > 7, we need to consider two cases based on the absolute value:
Case 1: 9 - 4x > 7
Solve this inequality by subtracting 9 from both sides:
-4x > 7 - 9
-4x > -2
Now, divide both sides by -4, remembering to reverse the inequality sign because we are dividing by a negative number:
x < -2/-4
x < 1/2
Case 2: -(9 - 4x) > 7
Solve this inequality by distributing the negative sign:
-9 + 4x > 7
Add 9 to both sides:
4x > 7 + 9
4x > 16
Now, divide both sides by 4:
x > 16/4
x > 4
So, we have found that x < 1/2 and x > 4 are the two separate solutions.
To express this solution set in interval notation, we write the two intervals as (1/2, 4) and (-infinity, 1/2) U (4, infinity).
Comparing this with the answer choices, the correct option is D.