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Solve: 3|2x−8| 6≥33

Write your solution in interval notation using reduced fractions.

User Scarlz
by
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1 Answer

5 votes

Answer: [19/2, -3/2]

Explanation:

To solve the inequality 3|2x - 8| ≥ 33, you need to consider two cases: one where the expression inside the absolute value is non-negative and one where it's negative.

Case 1: 2x - 8 is non-negative (greater than or equal to 0):

3(2x - 8) ≥ 33

Now, solve for x:

6x - 24 ≥ 33

Add 24 to both sides:

6x ≥ 57

Divide by 6:

x ≥ 57/6

Case 2: 2x - 8 is negative (less than 0):

3(-(2x - 8)) ≥ 33

Multiply -1 inside the absolute value:

-3(2x - 8) ≥ 33

Now, solve for x:

-6x + 24 ≥ 33

Subtract 24 from both sides:

-6x ≥ 9

Divide by -6 (and reverse the inequality sign because you're dividing by a negative number):

x ≤ -9/6

Now, simplify both fractions:

x ≥ 19/2 or x ≤ -3/2

In interval notation:

x ∈ [19/2, -3/2]

So, the solution in interval notation using reduced fractions is [19/2, -3/2].

User Porcupine
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