Solve for t |7t-4|=10

$| 7 t - 4 | = 10$

Step 1

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

$7 t - 4 = \pm 10$

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.

$7 t - 4 = 10$

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

Add $4$ to both sides of the equation.

$7 t = 10 + 4$

Add $10$ and $4$ .

$7 t = 14$

Divide each term in $7 t = 14$ by $7$ and simplify.

Divide each term in $7 t = 14$ by $7$ .

$\frac{7 t}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 t}{7} = \frac{14}{7}$

Divide $t$ by $1$ .

$t = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$t = 2$

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

$7 t - 4 = - 10$

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

Add $4$ to both sides of the equation.

$7 t = - 10 + 4$

Add $- 10$ and $4$ .

$7 t = - 6$

Divide each term in $7 t = - 6$ by $7$ and simplify.

Divide each term in $7 t = - 6$ by $7$ .

$\frac{7 t}{7} = \frac{- 6}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 t}{7} = \frac{- 6}{7}$

Divide $t$ by $1$ .

$t = \frac{- 6}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{6}{7}$

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

$t = 2, - \frac{6}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = 2, - \frac{6}{7}$

Decimal Form:

$t = 2, - 0.\overline{857142}$

Solve for t |7t-4|=10

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