QuestionSolve the absolute value equation. $|2 x-7|=11$

Studdy Solution

STEP 1

1. The expression involves the absolute value function, which returns the non-negative value of the expression inside it.
2. The absolute value equation can be split into two separate linear equations based on the definition of absolute value.
3. The solutions to these linear equations will be the solutions to the original absolute value equation.

STEP 2

1. Split the absolute value equation into two linear equations.
2. Solve each linear equation separately.
3. Combine the solutions from both equations.

STEP 3

Split the absolute value equation $|2x - 7| = 11$ into two separate linear equations based on the definition of absolute value:
$2x - 7 = 11$ $2x - 7 = -11$

STEP 4

Solve the first linear equation $2x - 7 = 11$ .
Add 7 to both sides: $2x - 7 + 7 = 11 + 7$ $2x = 18$

STEP 5

Divide both sides by 2: $x = \frac{18}{2}$ $x = 9$

STEP 6

Solve the second linear equation $2x - 7 = -11$ .
Add 7 to both sides: $2x - 7 + 7 = -11 + 7$ $2x = -4$

STEP 7

Divide both sides by 2: $x = \frac{-4}{2}$ $x = -2$

STEP 8

Combine the solutions from both equations. The solutions to the original absolute value equation are:
$x = 9 \quad \text{and} \quad x = -2$
Solution: The solutions to the equation $|2x - 7| = 11$ are $x = 9$ and $x = -2$ .

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