Question

What absolute value equation gives me the answer: x={-3,8}?

Answer 1

• |x - 2.5| = 5.5

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Let the equation be in the form:

• |x - a| = b

Then its solution is:

• x - a = b ⇒ x = a + b = 8
• x - a = - b ⇒ x = a - b = - 3

Add up the two equations:

• 2a = 8 - 3 ⇒ 2a = 5 ⇒ a = 2.5

Find b:

• b = 8 - 2.5 = 5.5

The equation is:

• |x - 2.5| = 5.5