Basic Math Examples

$480 (t - \frac{35}{60}) = 440 t$

Step 1

Simplify $480 (t - \frac{35}{60})$ .

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Step 1.1

Rewrite.

$0 + 0 + 480 (t - \frac{35}{60}) = 440 t$

Step 1.2

Simplify by adding zeros.

$480 (t - \frac{35}{60}) = 440 t$

Step 1.3

Cancel the common factor of $35$ and $60$ .

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Step 1.3.1

Factor $5$ out of $35$ .

$480 (t - \frac{5 (7)}{60}) = 440 t$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $5$ out of $60$ .

$480 (t - \frac{5 \cdot 7}{5 \cdot 12}) = 440 t$

Step 1.3.2.2

Cancel the common factor.

$480 (t - \frac{5 \cdot 7}{5 \cdot 12}) = 440 t$

Step 1.3.2.3

Rewrite the expression.

$480 (t - \frac{7}{12}) = 440 t$

Step 1.4

Apply the distributive property.

$480 t + 480 (- \frac{7}{12}) = 440 t$

Step 1.5

Cancel the common factor of $12$ .

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Step 1.5.1

Move the leading negative in $- \frac{7}{12}$ into the numerator.

$480 t + 480 (\frac{- 7}{12}) = 440 t$

Step 1.5.2

Factor $12$ out of $480$ .

$480 t + 12 (40) \frac{- 7}{12} = 440 t$

Step 1.5.3

Cancel the common factor.

$480 t + 12 \cdot 40 \frac{- 7}{12} = 440 t$

Step 1.5.4

Rewrite the expression.

$480 t + 40 \cdot - 7 = 440 t$

Step 1.6

Multiply $40$ by $- 7$ .

$480 t - 280 = 440 t$

Step 2

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

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Step 2.1

Subtract $440 t$ from both sides of the equation.

$480 t - 280 - 440 t = 0$

Step 2.2

Subtract $440 t$ from $480 t$ .

$40 t - 280 = 0$

Step 3

Add $280$ to both sides of the equation.

$40 t = 280$

Step 4

Divide each term in $40 t = 280$ by $40$ and simplify.

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Step 4.1

Divide each term in $40 t = 280$ by $40$ .

$\frac{40 t}{40} = \frac{280}{40}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $40$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{40 t}{40} = \frac{280}{40}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{280}{40}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $280$ by $40$ .

$t = 7$