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|2x-8| + 3 = 5 two solutions

1 Answer

5 votes

Answer:

The two solutions are 5 and 3

Explanation:

The equation of the absolute has two solutions because IxI = a means x = a and x = -a

Let us solve the question using this fact

I2x - 8I + 3 = 5

→ Subtract 3 from both sides

∴ I2x - 8I + 3 - 5 = 5 - 3

∴ I2x - 8I = 2

By using the fact above

1st solution

2x - 8 = 2

→ Add 8 to both sides

∴ 2x - 8 + 8 = 2 + 8

∴ 2x = 10

→ Divide both sides by 2 to find x

x = 5

2nd solution

2x - 8 = -2

→ Add 8 to both sides

∴ 2x - 8 + 8 = -2 + 8

∴ 2x = 6

→ Divide both sides by 2 to find x

x = 3

The two solutions are 5 and 3

User Tuergeist
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