Question

Which of the following are solutions to [x+3|= 4x - 7? Check all that apply.

Answer 1

Answer:

x = $\frac{10}{3}$

Step-by-step explanation:

Given

| x + 3 | = 4x - 7

The absolute value function always returns a positive value, however the expression inside can be positive or negative, thus

x + 3 = 4x - 7 OR - (x + 3) = 4x - 7

Solving the 2 equations

x + 3 = 4x - 7 ( subtract 4x from both sides )

- 3x + 3 = - 7 ( subtract 3 from both sides )

- 3x = - 10 ( divide both sides by - 3 )

x = $\frac{10}{3}$

OR

- (x + 3) = 4x - 7, that is

- x - 3 = 4x - 7 ( subtract 4x from both sides )

- 5x - 3 = - 7 ( add 3 to both sides )

- 5x = - 4 ( divide both sides by - 5 )

x = $\frac{4}5}$

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As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = $\frac{10}{3}$

| $\frac{10}{3}$ + 3 | = | $\frac{19}{3}$ | = $\frac{19}{3}$ and 4($\frac{10}{3}$ ) - 7 = $\frac{40}{3}$ - $\frac{21}{3}$ = $\frac{19}{3}$

left side = right side

Thus x = $\frac{10}{3}$ is a solution

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x = $\frac{4}{5}$

| $\frac{4}{5}$ + 3 | = | $\frac{19}{5}$ | = $\frac{19}{5}$ and 4($\frac{4}{5}$ ) - 7 = $\frac{16}{5}$ - $\frac{35}{5}$ = - $\frac{19}{5}$

left side ≠ right side

Thus x = $\frac{4}{5}$ is an extraneous solution