Basic Math Examples

\frac{1}{4} \cdot (8 t - 9) = \frac{7}{4} t - \frac{t + 9}{8}

$\frac{1}{4} \cdot (8 t - 9) = \frac{7}{4} t - \frac{t + 9}{8}$

Step 1

Since

t

$t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

\frac{7}{4} t - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7}{4} t - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2

Simplify

\frac{7}{4} t - \frac{t + 9}{8}

$\frac{7}{4} t - \frac{t + 9}{8}$ .

Tap for more steps...

Step 2.1

Combine

\frac{7}{4}

$\frac{7}{4}$ and

t

$t$ .

\frac{7 t}{4} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t}{4} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.2

To write

\frac{7 t}{4}

$\frac{7 t}{4}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7 t}{4} \cdot \frac{2}{2} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t}{4} \cdot \frac{2}{2} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.3

Write each expression with a common denominator of

8

$8$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 2.3.1

Multiply

\frac{7 t}{4}

$\frac{7 t}{4}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7 t \cdot 2}{4 \cdot 2} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t \cdot 2}{4 \cdot 2} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.3.2

Multiply

4

$4$ by

2

$2$ .

\frac{7 t \cdot 2}{8} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t \cdot 2}{8} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

\frac{7 t \cdot 2}{8} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t \cdot 2}{8} - \frac{t + 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.4

Combine the numerators over the common denominator.

\frac{7 t \cdot 2 - (t + 9)}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{7 t \cdot 2 - (t + 9)}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply

2

$2$ by

7

$7$ .

\frac{14 t - (t + 9)}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{14 t - (t + 9)}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.5.2

Apply the distributive property.

\frac{14 t - t - 1 \cdot 9}{8} = \frac{1}{4} \cdot (8 t - 9)

$\frac{14 t - t - 1 \cdot 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.5.3

Multiply

$- 1$ by

$9$ .

$\frac{14 t - t - 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 2.5.4

Subtract

$t$ from

$14 t$ .

$\frac{13 t - 9}{8} = \frac{1}{4} \cdot (8 t - 9)$

Step 3

Simplify

$\frac{1}{4} \cdot (8 t - 9)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$\frac{13 t - 9}{8} = \frac{1}{4} (8 t) + \frac{1}{4} \cdot - 9$

Step 3.2

Cancel the common factor of

$4$ .

Tap for more steps...

Step 3.2.1

Factor

$4$ out of

$8 t$ .

$\frac{13 t - 9}{8} = \frac{1}{4} (4 (2 t)) + \frac{1}{4} \cdot - 9$

Step 3.2.2

Cancel the common factor.

$\frac{13 t - 9}{8} = \frac{1}{4} (4 (2 t)) + \frac{1}{4} \cdot - 9$

Step 3.2.3

Rewrite the expression.

$\frac{13 t - 9}{8} = 2 t + \frac{1}{4} \cdot - 9$

Step 3.3

Combine

$\frac{1}{4}$ and

$- 9$ .

$\frac{13 t - 9}{8} = 2 t + \frac{- 9}{4}$

Step 3.4

Move the negative in front of the fraction.

$\frac{13 t - 9}{8} = 2 t - \frac{9}{4}$

Step 4

Move all terms containing

$t$ to the left side of the equation.

Tap for more steps...

Step 4.1

Subtract

$2 t$ from both sides of the equation.

$\frac{13 t - 9}{8} - 2 t = - \frac{9}{4}$

Step 4.2

To write

$- 2 t$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{13 t - 9}{8} - 2 t \cdot \frac{8}{8} = - \frac{9}{4}$

Step 4.3

Combine

$- 2 t$ and

$\frac{8}{8}$ .

$\frac{13 t - 9}{8} + \frac{- 2 t \cdot 8}{8} = - \frac{9}{4}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{13 t - 9 - 2 t \cdot 8}{8} = - \frac{9}{4}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply

$8$ by

$- 2$ .

$\frac{13 t - 9 - 16 t}{8} = - \frac{9}{4}$

Step 4.5.2

Subtract

$16 t$ from

$13 t$ .

$\frac{- 3 t - 9}{8} = - \frac{9}{4}$

Step 4.5.3

Factor

$3$ out of

$- 3 t - 9$ .

Tap for more steps...

Step 4.5.3.1

Factor

$3$ out of

$- 3 t$ .

$\frac{3 (- t) - 9}{8} = - \frac{9}{4}$

Step 4.5.3.2

Factor

$3$ out of

$- 9$ .

$\frac{3 (- t) + 3 (- 3)}{8} = - \frac{9}{4}$

Step 4.5.3.3

Factor

$3$ out of

$3 (- t) + 3 (- 3)$ .

$\frac{3 (- t - 3)}{8} = - \frac{9}{4}$

Step 4.6

Factor

$- 1$ out of

$- t$ .

$\frac{3 (- (t) - 3)}{8} = - \frac{9}{4}$

Step 4.7

Rewrite

$- 3$ as

$- 1 (3)$ .

$\frac{3 (- (t) - 1 (3))}{8} = - \frac{9}{4}$

Step 4.8

Factor

$- 1$ out of

$- (t) - 1 (3)$ .

$\frac{3 (- (t + 3))}{8} = - \frac{9}{4}$

Step 4.9

Rewrite

$- (t + 3)$ as

$- 1 (t + 3)$ .

$\frac{3 (- 1 (t + 3))}{8} = - \frac{9}{4}$

Step 4.10

Move the negative in front of the fraction.

$- \frac{3 (t + 3)}{8} = - \frac{9}{4}$

Step 5

Multiply both sides of the equation by

$- \frac{8}{3}$ .

$- \frac{8}{3} (- \frac{3 (t + 3)}{8}) = - \frac{8}{3} (- \frac{9}{4})$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify

$- \frac{8}{3} (- \frac{3 (t + 3)}{8})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of

$8$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in

$- \frac{8}{3}$ into the numerator.

$\frac{- 8}{3} (- \frac{3 (t + 3)}{8}) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.1.2

Move the leading negative in

$- \frac{3 (t + 3)}{8}$ into the numerator.

$\frac{- 8}{3} \cdot \frac{- 3 (t + 3)}{8} = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.1.3

Factor

$8$ out of

$- 8$ .

$\frac{8 (- 1)}{3} \cdot \frac{- 3 (t + 3)}{8} = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{3} \cdot \frac{- 3 (t + 3)}{8} = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 (t + 3)) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.2

Cancel the common factor of

$3$ .

Tap for more steps...

Step 6.1.1.2.1

Factor

$3$ out of

$- 3 (t + 3)$ .

$\frac{- 1}{3} (3 (- (t + 3))) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- (t + 3))) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.2.3

Rewrite the expression.

$- - (t + 3) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply

$- 1$ by

$- 1$ .

$1 (t + 3) = - \frac{8}{3} (- \frac{9}{4})$

Step 6.1.1.3.2

Multiply

$t + 3$ by

$1$ .

$t + 3 = - \frac{8}{3} (- \frac{9}{4})$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify

$- \frac{8}{3} (- \frac{9}{4})$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of

$4$ .

Tap for more steps...

Step 6.2.1.1.1

Move the leading negative in

$- \frac{8}{3}$ into the numerator.

$t + 3 = \frac{- 8}{3} (- \frac{9}{4})$

Step 6.2.1.1.2

Move the leading negative in

$- \frac{9}{4}$ into the numerator.

$t + 3 = \frac{- 8}{3} \cdot \frac{- 9}{4}$

Step 6.2.1.1.3

Factor

$4$ out of

$- 8$ .

$t + 3 = \frac{4 (- 2)}{3} \cdot \frac{- 9}{4}$

Step 6.2.1.1.4

Cancel the common factor.

$t + 3 = \frac{4 \cdot - 2}{3} \cdot \frac{- 9}{4}$

Step 6.2.1.1.5

Rewrite the expression.

$t + 3 = \frac{- 2}{3} \cdot - 9$

Step 6.2.1.2

Cancel the common factor of

$3$ .

Tap for more steps...

Step 6.2.1.2.1

Factor

$3$ out of

$- 9$ .

$t + 3 = \frac{- 2}{3} \cdot (3 (- 3))$

Step 6.2.1.2.2

Cancel the common factor.

$t + 3 = \frac{- 2}{3} \cdot (3 \cdot - 3)$

Step 6.2.1.2.3

Rewrite the expression.

$t + 3 = - 2 \cdot - 3$

Step 6.2.1.3

Multiply

$- 2$ by

$- 3$ .

$t + 3 = 6$

Step 7

Move all terms not containing

$t$ to the right side of the equation.

Tap for more steps...

Step 7.1

Subtract

$3$ from both sides of the equation.

$t = 6 - 3$

Step 7.2

Subtract

$3$ from

$6$ .

$t = 3$