Solve for t |5t-2|=8

$| 5 t - 2 | = 8$

Step 1

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

$5 t - 2 = \pm 8$

Step 2

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.

$5 t - 2 = 8$

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

Add $2$ to both sides of the equation.

$5 t = 8 + 2$

Add $8$ and $2$ .

$5 t = 10$

Divide each term in $5 t = 10$ by $5$ and simplify.

Divide each term in $5 t = 10$ by $5$ .

$\frac{5 t}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 t}{5} = \frac{10}{5}$

Divide $t$ by $1$ .

$t = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$t = 2$

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

$5 t - 2 = - 8$

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

Add $2$ to both sides of the equation.

$5 t = - 8 + 2$

Add $- 8$ and $2$ .

$5 t = - 6$

Divide each term in $5 t = - 6$ by $5$ and simplify.

Divide each term in $5 t = - 6$ by $5$ .

$\frac{5 t}{5} = \frac{- 6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 t}{5} = \frac{- 6}{5}$

Divide $t$ by $1$ .

$t = \frac{- 6}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{6}{5}$

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

$t = 2, - \frac{6}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = 2, - \frac{6}{5}$

Decimal Form:

$t = 2, - 1.2$

Mixed Number Form:

$t = 2, - 1 \frac{1}{5}$

Solve for t |5t-2|=8

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