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scoundrel [369]
2 years ago
8

Given g(x)=|-3x+16|, if g(x)=18, find x.

Mathematics
2 answers:
LenaWriter [7]2 years ago
8 0

Answer:

x = - \frac{2}{3} , x = \frac{34}{3}

Step-by-step explanation:

The absolute value function always gives a positive value, however, the expression inside can be positive or negative, that is

- 3x + 16 = 18 or -(- 3x + 16) = 18

Solving

- 3x + 16 = 18 ( subtract 16 from both sides )

- 3x = 2 ( divide both sides by - 3 )

x = - \frac{2}{3}

or

-(- 3x + 16) = 18

3x - 16 = 18 ( add 16 to both sides )

3x = 34 ( divide both sides by 3 )

x = \frac{34}{4}

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

| - 3(- \frac{2}{3} ) + 16 | = | 2 + 16 | = | 18 | = 18 ← True

| - 3(\frac{34}{3} ) + 16 | = | - 34 + 16 | = | - 18 | = 18 ← True

Thus x = - \frac{2}{3} and x = \frac{34}{3} are the solutions

Ne4ueva [31]2 years ago
8 0

<u>Given</u>:-

g(x)=18

<u>To find</u><em>:-</em>

x

<u>Solution</u>:-

g(x)=(-3x+16)

18=-3x+16

18-16=-3x

2=-3x

x=2/-3

hope it helps you!

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Answer:

x = 12

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define equation</u>

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  1. Distribute -2:                    -2x + 8 = -16
  2. Isolate <em>x</em> term:                  -2x = -24
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<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    -2(12 - 4) = -16
  2. Subtract:                       -2(8) = -16
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Here we see that -16 does indeed equal -16.

∴ x = 12 is a solution of the equation.

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