Which of the following are solutions to [x+3|= 4x - 7? Check all that apply.
A. X = 1/2
B. x = -1/3
1 c. x= -11 /
D. x = 10

x =

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 =

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 =

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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 =

| + 3 | = | | = and 4( ) - 7 = - =

left side = right side

Thus x = is a solution

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x =

| + 3 | = | | = and 4( ) - 7 = - = -

left side ≠ right side

Thus x = is an extraneous solution