Basic Math Examples

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

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1}{2} \cdot (4 t - 7) \cdot 4$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $4 t$ .

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

Step 2.1.1.2.2

Cancel the common factor.

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

Step 2.1.1.2.3

Rewrite the expression.

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

Step 2.1.1.3

Combine $\frac{1}{2}$ and $- 7$ .

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

Step 2.1.1.4

Move the negative in front of the fraction.

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Multiply $4$ by $2$ .

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

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

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

Step 2.1.1.7.2

Factor $2$ out of $4$ .

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

Step 2.1.1.7.3

Cancel the common factor.

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

Step 2.1.1.7.4

Rewrite the expression.

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

Step 2.1.1.8

Multiply $- 7$ by $2$ .

$8 t - 14 = \frac{t + 7}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$8 t - 14 = \frac{t + 7}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$8 t - 14 = t + 7$

Step 3

Solve for $t$ .

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Step 3.1

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

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Step 3.1.1

Subtract $t$ from both sides of the equation.

$8 t - 14 - t = 7$

Step 3.1.2

Subtract $t$ from $8 t$ .

$7 t - 14 = 7$

Step 3.2

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

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Step 3.2.1

Add $14$ to both sides of the equation.

$7 t = 7 + 14$

Step 3.2.2

Add $7$ and $14$ .

$7 t = 21$

Step 3.3

Divide each term in $7 t = 21$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 t = 21$ by $7$ .

$\frac{7 t}{7} = \frac{21}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 t}{7} = \frac{21}{7}$

Step 3.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{21}{7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $21$ by $7$ .

$t = 3$