Solve for t |3t-2|=10

$| 3 t - 2 | = 10$

Step 1

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

$3 t - 2 = \pm 10$

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.

$3 t - 2 = 10$

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

Add $2$ to both sides of the equation.

$3 t = 10 + 2$

Add $10$ and $2$ .

$3 t = 12$

Divide each term in $3 t = 12$ by $3$ and simplify.

Divide each term in $3 t = 12$ by $3$ .

$\frac{3 t}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{12}{3}$

Divide $t$ by $1$ .

$t = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$t = 4$

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

$3 t - 2 = - 10$

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

Add $2$ to both sides of the equation.

$3 t = - 10 + 2$

Add $- 10$ and $2$ .

$3 t = - 8$

Divide each term in $3 t = - 8$ by $3$ and simplify.

Divide each term in $3 t = - 8$ by $3$ .

$\frac{3 t}{3} = \frac{- 8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{- 8}{3}$

Divide $t$ by $1$ .

$t = \frac{- 8}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{8}{3}$

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

$t = 4, - \frac{8}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = 4, - \frac{8}{3}$

Decimal Form:

$t = 4, - 2.\overline{6}$

Mixed Number Form:

$t = 4, - 2 \frac{2}{3}$

Solve for t |3t-2|=10

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