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.)
C. The solution is x≤
or x≥
D. The solution is all real numbers.
- (Type integers or simplified fractions.)
To solve the inequality -35 + |4x-8| ≤ -7, we can split the inequality into two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 4x-8 ≥ 0 (expression inside absolute value is positive)
In this case, we have -35 + (4x-8) ≤ -7.
Simplifying this, we get 4x - 43 ≤ -7.
Adding 43 to both sides, we have 4x ≤ 36.
Dividing both sides by 4, we get x ≤ 9.
Case 2: 4x-8 < 0 (expression inside absolute value is negative)
In this case, we have -35 + (-(4x-8)) ≤ -7.
Simplifying this, we get -35 - 4x + 8 ≤ -7.
Combining like terms, we have -4x - 27 ≤ -7.
Adding 27 to both sides, we have -4x ≤ 20.
Dividing both sides by -4 (and reversing the inequality), we get x ≥ -5.
Putting our solutions together, we have x ≤ 9 or x ≥ -5.
Therefore, the solution is x ≤ 9 or x ≥ -5.