Basic Math Examples

$\frac{7 t + 1}{4} = \frac{t + 5}{8} + \frac{t - 3}{8}$

Step 1

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

$\frac{t + 5}{8} + \frac{t - 3}{8} = \frac{7 t + 1}{4}$

Step 2

Multiply both sides by $4$ .

$(\frac{t + 5}{8} + \frac{t - 3}{8}) \cdot 4 = \frac{7 t + 1}{4} \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(\frac{t + 5}{8} + \frac{t - 3}{8}) \cdot 4$ .

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Step 3.1.1.1

Combine the numerators over the common denominator.

$\frac{t + 5 + t - 3}{8} \cdot 4 = \frac{7 t + 1}{4} \cdot 4$

Step 3.1.1.2

Add $t$ and $t$ .

$\frac{2 t + 5 - 3}{8} \cdot 4 = \frac{7 t + 1}{4} \cdot 4$

Step 3.1.1.3

Subtract $3$ from $5$ .

$\frac{2 t + 2}{8} \cdot 4 = \frac{7 t + 1}{4} \cdot 4$

Step 3.1.1.4

Factor $2$ out of $2 t + 2$ .

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Step 3.1.1.4.1

Factor $2$ out of $2 t$ .

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

Step 3.1.1.4.2

Factor $2$ out of $2$ .

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

Step 3.1.1.4.3

Factor $2$ out of $2 (t) + 2 (1)$ .

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

Step 3.1.1.5

Cancel the common factor of $4$ .

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Step 3.1.1.5.1

Factor $4$ out of $8$ .

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

Step 3.1.1.5.2

Cancel the common factor.

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

Step 3.1.1.5.3

Rewrite the expression.

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

Step 3.1.1.6

Cancel the common factor of $2$ .

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Step 3.1.1.6.1

Cancel the common factor.

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

Step 3.1.1.6.2

Divide $t + 1$ by $1$ .

$t + 1 = \frac{7 t + 1}{4} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$t + 1 = \frac{7 t + 1}{4} \cdot 4$

Step 3.2.1.2

Rewrite the expression.

$t + 1 = 7 t + 1$

Step 4

Solve for $t$ .

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Step 4.1

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

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Step 4.1.1

Subtract $7 t$ from both sides of the equation.

$t + 1 - 7 t = 1$

Step 4.1.2

Subtract $7 t$ from $t$ .

$- 6 t + 1 = 1$

Step 4.2

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

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$- 6 t = 1 - 1$

Step 4.2.2

Subtract $1$ from $1$ .

$- 6 t = 0$

Step 4.3

Divide each term in $- 6 t = 0$ by $- 6$ and simplify.

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Step 4.3.1

Divide each term in $- 6 t = 0$ by $- 6$ .

$\frac{- 6 t}{- 6} = \frac{0}{- 6}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 6$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 6 t}{- 6} = \frac{0}{- 6}$

Step 4.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{0}{- 6}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $0$ by $- 6$ .

$t = 0$