Question5) $|-x+9|=3$
Solution $=$

Studdy Solution

STEP 1

1. The absolute value equation $|-x + 9| = 3$ involves an absolute value expression, which means it can be split into two separate linear equations.
2. The solutions to these equations will be real numbers.

STEP 2

1. Split the absolute value equation $|-x + 9| = 3$ into two separate linear equations.
2. Solve each linear equation for $x$ .
3. Verify the solutions by substituting them back into the original equation.

STEP 3

Split the absolute value equation $|-x + 9| = 3$ into two separate linear equations:
$-x + 9 = 3 \quad \text{or} \quad -x + 9 = -3$

STEP 4

Solve the first equation $-x + 9 = 3$ for $x$ .
$-x + 9 = 3$
Subtract 9 from both sides:
$-x = 3 - 9$
Simplify the right side:
$-x = -6$
Multiply both sides by $-1$ :
$x = 6$

STEP 5

Solve the second equation $-x + 9 = -3$ for $x$ .
$-x + 9 = -3$
Subtract 9 from both sides:
$-x = -3 - 9$
Simplify the right side:
$-x = -12$
Multiply both sides by $-1$ :
$x = 12$

STEP 6

Verify the solutions $x = 6$ and $x = 12$ by substituting them back into the original equation.
For $x = 6$ :
$|-6 + 9| = |3| = 3$
For $x = 12$ :
$|-12 + 9| = |-3| = 3$
Both solutions satisfy the original equation.
Solution = $\{6, 12\}$

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