Solve for t 19/24=-5/6t-1/4

$\frac{19}{24} = - \frac{5}{6} t - \frac{1}{4}$

Step 1

Rewrite the equation as $- \frac{5}{6} t - \frac{1}{4} = \frac{19}{24}$ .

$- \frac{5}{6} t - \frac{1}{4} = \frac{19}{24}$

Step 2

Simplify each term.

Combine $t$ and $\frac{5}{6}$ .

$- \frac{t \cdot 5}{6} - \frac{1}{4} = \frac{19}{24}$

Move $5$ to the left of $t$ .

$- \frac{5 t}{6} - \frac{1}{4} = \frac{19}{24}$

Step 3

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

Add $\frac{1}{4}$ to both sides of the equation.

$- \frac{5 t}{6} = \frac{19}{24} + \frac{1}{4}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{5 t}{6} = \frac{19}{24} + \frac{1}{4} \cdot \frac{6}{6}$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{6}{6}$ .

$- \frac{5 t}{6} = \frac{19}{24} + \frac{6}{4 \cdot 6}$

Multiply $4$ by $6$ .

$- \frac{5 t}{6} = \frac{19}{24} + \frac{6}{24}$

Combine the numerators over the common denominator.

$- \frac{5 t}{6} = \frac{19 + 6}{24}$

Add $19$ and $6$ .

$- \frac{5 t}{6} = \frac{25}{24}$

Step 4

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5 t}{6}) = - \frac{6}{5} \cdot \frac{25}{24}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{5} (- \frac{5 t}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{5 t}{6}) = - \frac{6}{5} \cdot \frac{25}{24}$

Move the leading negative in $- \frac{5 t}{6}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 5 t}{6} = - \frac{6}{5} \cdot \frac{25}{24}$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{5} \cdot \frac{- 5 t}{6} = - \frac{6}{5} \cdot \frac{25}{24}$

Cancel the common factor.

$\frac{6 \cdot - 1}{5} \cdot \frac{- 5 t}{6} = - \frac{6}{5} \cdot \frac{25}{24}$

Rewrite the expression.

$\frac{- 1}{5} (- 5 t) = - \frac{6}{5} \cdot \frac{25}{24}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 t$ .

$\frac{- 1}{5} (5 (- t)) = - \frac{6}{5} \cdot \frac{25}{24}$

Cancel the common factor.

$\frac{- 1}{5} (5 (- t)) = - \frac{6}{5} \cdot \frac{25}{24}$

Rewrite the expression.

$- - t = - \frac{6}{5} \cdot \frac{25}{24}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 t = - \frac{6}{5} \cdot \frac{25}{24}$

Multiply $t$ by $1$ .

$t = - \frac{6}{5} \cdot \frac{25}{24}$

Simplify the right side.

Simplify $- \frac{6}{5} \cdot \frac{25}{24}$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$t = \frac{- 6}{5} \cdot \frac{25}{24}$

Factor $6$ out of $- 6$ .

$t = \frac{6 (- 1)}{5} \cdot \frac{25}{24}$

Factor $6$ out of $24$ .

$t = \frac{6 \cdot - 1}{5} \cdot \frac{25}{6 \cdot 4}$

Cancel the common factor.

$t = \frac{6 \cdot - 1}{5} \cdot \frac{25}{6 \cdot 4}$

Rewrite the expression.

$t = \frac{- 1}{5} \cdot \frac{25}{4}$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$t = \frac{- 1}{5} \cdot \frac{5 (5)}{4}$

Cancel the common factor.

$t = \frac{- 1}{5} \cdot \frac{5 \cdot 5}{4}$

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$t = - 1.25$

Mixed Number Form:

$t = - 1 \frac{1}{4}$

Solve for t 19/24=-5/6t-1/4

Related Questions

Support LCMGCF.com by disabling your adblocker.