Question

The equation 2|3x - 1] = 10 has two solutions, one positive and one negative. Solve the equation to find the solutions.

Enter your answers in the boxes.
X=

Answer 1

Answers: x = 2 or x = -4/3

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Work Shown:

2|3x - 1| = 10

|3x - 1| = 10/2

|3x - 1| = 5

3x - 1 = 5 or 3x - 1 = -5

3x = 5+1 or 3x = -5+1

3x = 6 or 3x = -4

x = 6/3 or x = -4/3

x = 2 or x = -4/3

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Check:

Plug in x = 2 to get...

2|3x - 1| = 10

2|3*2 - 1| = 10

2|6-1| = 10

2|5| = 10

2*5 = 10

10 = 10

This confirms x = 2.

Repeat for x = -4/3

2|3x - 1| = 10

2|3*(-4/3) - 1| = 10

2|-4-1| = 10

2|-5| = 10

2*5 = 10

10 = 10

This confirms x = -4/3

Both solutions are confirmed.