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B. Solve the following.

1.) |2x - 3| = 5
2.) |x - 5| = 12​

User Pastaleg
by
7.6k points

1 Answer

4 votes

Answer:

1. x = 4 and x = -1.

2. x = 17 and x = -7.

Explanation:

1.) |2x - 3| = 5

To solve this equation, we need to consider two cases: when 2x - 3 is positive and when it is negative.

Case 1: 2x - 3 ≥ 0

If 2x - 3 is positive, then we have:

2x - 3 = 5

Solving for x, we get:

x = 4

Case 2: 2x - 3 < 0

If 2x - 3 is negative, then we have:

-(2x - 3) = 5

Simplifying, we get:

-2x + 3 = 5

Solving for x, we get:

x = -1

Therefore, the solutions to the equation |2x - 3| = 5 are x = 4 and x = -1.

2.) |x - 5| = 12

To solve this equation, we again need to consider two cases: when x - 5 is positive and when it is negative.

Case 1: x - 5 ≥ 0

If x - 5 is positive, then we have:

x - 5 = 12

Solving for x, we get:

x = 17

Case 2: x - 5 < 0

If x - 5 is negative, then we have:

-(x - 5) = 12

Simplifying, we get:

-x + 5 = 12

Solving for x, we get:

x = -7

Therefore, the solutions to the equation |x - 5| = 12 are x = 17 and x = -7.

User BuckFilledPlatypus
by
7.6k points

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