Solve for t 3/4|8t-12|=6(t-1)

$\frac{3}{4} | 8 t - 12 | = 6 (t - 1)$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} (\frac{3}{4} | 8 t - 12 |) = \frac{4}{3} (6 (t - 1))$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} (\frac{3}{4} | 8 t - 12 |)$ .

Combine $\frac{3}{4}$ and $| 8 t - 12 |$ .

$\frac{4}{3} \cdot \frac{3 | 8 t - 12 |}{4} = \frac{4}{3} (6 (t - 1))$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 | 8 t - 12 |}{4} = \frac{4}{3} (6 (t - 1))$

Rewrite the expression.

$\frac{1}{3} (3 | 8 t - 12 |) = \frac{4}{3} (6 (t - 1))$

Cancel the common factor of $3$ .

Factor $3$ out of $3 | 8 t - 12 |$ .

$\frac{1}{3} (3 | 8 t - 12 |) = \frac{4}{3} (6 (t - 1))$

Cancel the common factor.

$\frac{1}{3} (3 | 8 t - 12 |) = \frac{4}{3} (6 (t - 1))$

Rewrite the expression.

$| 8 t - 12 | = \frac{4}{3} (6 (t - 1))$

Simplify the right side.

Simplify $\frac{4}{3} (6 (t - 1))$ .

Cancel the common factor of $3$ .

Factor $3$ out of $6 (t - 1)$ .

$| 8 t - 12 | = \frac{4}{3} (3 (2 (t - 1)))$

Cancel the common factor.

$| 8 t - 12 | = \frac{4}{3} (3 (2 (t - 1)))$

Rewrite the expression.

$| 8 t - 12 | = 4 (2 (t - 1))$

Multiply $2$ by $4$ .

$| 8 t - 12 | = 8 (t - 1)$

Apply the distributive property.

$| 8 t - 12 | = 8 t + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$| 8 t - 12 | = 8 t - 8$

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

$8 t - 12 = \pm (8 t - 8)$

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.

$8 t - 12 = 8 t - 8$

Move all terms containing $t$ to the left side of the equation.

Subtract $8 t$ from both sides of the equation.

$8 t - 12 - 8 t = - 8$

Combine the opposite terms in $8 t - 12 - 8 t$ .

Subtract $8 t$ from $8 t$ .

$0 - 12 = - 8$

Subtract $12$ from $0$ .

$- 12 = - 8$

Since $- 12 \neq - 8$ , there are no solutions.

No solution

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

$8 t - 12 = - (8 t - 8)$

Simplify $- (8 t - 8)$ .

Rewrite.

$8 t - 12 = 0 + 0 - (8 t - 8)$

Simplify by adding zeros.

$8 t - 12 = - (8 t - 8)$

Apply the distributive property.

$8 t - 12 = - (8 t) - - 8$

Multiply.

Multiply $8$ by $- 1$ .

$8 t - 12 = - 8 t - - 8$

Multiply $- 1$ by $- 8$ .

$8 t - 12 = - 8 t + 8$

Move all terms containing $t$ to the left side of the equation.

Add $8 t$ to both sides of the equation.

$8 t - 12 + 8 t = 8$

Add $8 t$ and $8 t$ .

$16 t - 12 = 8$

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

Add $12$ to both sides of the equation.

$16 t = 8 + 12$

Add $8$ and $12$ .

$16 t = 20$

Divide each term in $16 t = 20$ by $16$ and simplify.

Divide each term in $16 t = 20$ by $16$ .

$\frac{16 t}{16} = \frac{20}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 t}{16} = \frac{20}{16}$

Divide $t$ by $1$ .

$t = \frac{20}{16}$

Simplify the right side.

Cancel the common factor of $20$ and $16$ .

Factor $4$ out of $20$ .

$t = \frac{4 (5)}{16}$

Cancel the common factors.

Factor $4$ out of $16$ .

$t = \frac{4 \cdot 5}{4 \cdot 4}$

Cancel the common factor.

$t = \frac{4 \cdot 5}{4 \cdot 4}$

Rewrite the expression.

$t = \frac{5}{4}$

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

$t =$

Solve for t 3/4|8t-12|=6(t-1)

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