Solve for x: 6|1 - 5x| - 9 = 57
Understand the Problem
The question is asking to solve an absolute value equation. You will need to isolate the absolute value expression, solve for both the positive and negative cases, and calculate the final answer.
Answer
$x = -2, \frac{12}{5}$
Answer for screen readers
$x = -2, \frac{12}{5}$
Steps to Solve
- Isolate the absolute value term
First, isolate the absolute value expression by adding 9 to both sides of the equation:
$6|1 - 5x| - 9 + 9 = 57 + 9$
$6|1 - 5x| = 66$
- Divide to further isolate the absolute value
Divide both sides by 6
$\frac{6|1 - 5x|}{6} = \frac{66}{6}$
$|1 - 5x| = 11$
- Solve for the positive case
Set the expression inside the absolute value equal to 11 and solve for $x$:
$1 - 5x = 11$
Subtract 1 from both sides:
$1 - 5x - 1 = 11 - 1$
$-5x = 10$
Divide both sides by -5:
$\frac{-5x}{-5} = \frac{10}{-5}$
$x = -2$
- Solve for the negative case
Set the expression inside the absolute value equal to -11 and solve for $x$:
$1 - 5x = -11$
Subtract 1 from both sides:
$1 - 5x - 1 = -11 - 1$
$-5x = -12$
Divide both sides by -5:
$\frac{-5x}{-5} = \frac{-12}{-5}$
$x = \frac{12}{5}$
$x = -2, \frac{12}{5}$
More Information
Absolute value equations will give you two answers in most cases, one positive and one negative.
Tips
A common mistake is forgetting to solve for both the positive and negative cases of the absolute value. Always remember that the expression inside the absolute value can be equal to both the positive and negative values of the number on the other side of the equation. Another common mistake is not properly isolating the absolute value expression before splitting the equation into two cases. Make sure the absolute value is isolated on one side of the equation before proceeding.
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