Algebra Examples

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

Step 1

Multiply both sides of the equation by $7$ .

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

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $7 (\frac{1}{7} \cdot (t - 9))$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Combine $\frac{1}{7}$ and $t$ .

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

Step 2.1.1.3

Combine $\frac{1}{7}$ and $- 9$ .

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

Step 2.1.1.4

Move the negative in front of the fraction.

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $7$ .

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Step 2.1.1.6.1

Cancel the common factor.

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

Step 2.1.1.6.2

Rewrite the expression.

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

Step 2.1.1.7

Cancel the common factor of $7$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

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

Step 2.1.1.7.2

Cancel the common factor.

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

Step 2.1.1.7.3

Rewrite the expression.

$t - 9 = 7 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $7$ by $4$ .

$t - 9 = 28$

Step 3

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

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Step 3.1

Add $9$ to both sides of the equation.

$t = 28 + 9$

Step 3.2

Add $28$ and $9$ .

$t = 37$