Solve the Absolute Value Inequality for a |1-5a|=29

$| 1 - 5 a | = 29$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$1 - 5 a = \pm 29$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$1 - 5 a = 29$

Move all terms not containing $a$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- 5 a = 29 - 1$

Subtract $1$ from $29$ .

$- 5 a = 28$

Divide each term in $- 5 a = 28$ by $- 5$ and simplify.

Divide each term in $- 5 a = 28$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{28}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{28}{- 5}$

Divide $a$ by $1$ .

$a = \frac{28}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{28}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$1 - 5 a = - 29$

Move all terms not containing $a$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- 5 a = - 29 - 1$

Subtract $1$ from $- 29$ .

$- 5 a = - 30$

Divide each term in $- 5 a = - 30$ by $- 5$ and simplify.

Divide each term in $- 5 a = - 30$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{- 30}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{- 30}{- 5}$

Divide $a$ by $1$ .

$a = \frac{- 30}{- 5}$

Simplify the right side.

Divide $- 30$ by $- 5$ .

$a = 6$

The complete solution is the result of both the positive and negative portions of the solution.

$a = - \frac{28}{5}, 6$

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{28}{5}, 6$

Decimal Form:

$a = - 5.6, 6$

Mixed Number Form:

$a = - 5 \frac{3}{5}, 6$

Solve the Absolute Value Inequality for a |1-5a|=29

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