Solve the inequality. Graph the solutions.
- 35 + |4x-8| ≤ -7
Select the correct choice below and fill in any answer boxes in your choice.
• A. The solution is
=X=
- (Type integers or simplified fractions.)
• B. The solution is x=
- (Type an integer or a simplified fraction.)
O. C. The solution is x≤
or x≥
O D. The solution is all real numbers.
- (Type integers or simplified fractions.)
To solve the inequality - 35 + |4x-8| ≤ -7, we can split it into two cases:
Case 1: 4x-8 ≥ 0
In this case, |4x-8| = 4x-8, so the inequality becomes -35 + 4x - 8 ≤ -7.
Simplifying it gives 4x - 43 ≤ -7. Adding 43 to both sides, we get 4x ≤ 36. Dividing both sides by 4 gives x ≤ 9.
Case 2: 4x-8 < 0
In this case, |4x-8| = -(4x-8) = -4x + 8, so the inequality becomes -35 - 4x + 8 ≤ -7.
Simplifying it gives -4x - 27 ≤ -7. Adding 27 to both sides, we get -4x ≤ 20. Dividing both sides by -4 (and flipping the inequality sign since we are dividing by a negative number) gives x ≥ -5.
Therefore, the solution to the inequality is x ≤ 9 or x ≥ -5.
This can be written as x ≤ 9 or x ≤ -5 (since the second option is already included in the first option).
So, the correct choice is:
C. The solution is x ≤ 9 or x ≤ -5.