Pre-Algebra Examples

$21 = \frac{7^{2} - t}{2}$

Step 1

Rewrite the equation as $\frac{7^{2} - t}{2} = 21$ .

$\frac{7^{2} - t}{2} = 21$

Step 2

Multiply both sides by $2$ .

$\frac{7^{2} - t}{2} \cdot 2 = 21 \cdot 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{7^{2} - t}{2} \cdot 2$ .

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Step 3.1.1.1

Raise $7$ to the power of $2$ .

$\frac{49 - t}{2} \cdot 2 = 21 \cdot 2$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{49 - t}{2} \cdot 2 = 21 \cdot 2$

Step 3.1.1.2.2

Rewrite the expression.

$49 - t = 21 \cdot 2$

Step 3.1.1.3

Reorder $49$ and $- t$ .

$- t + 49 = 21 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $21$ by $2$ .

$- t + 49 = 42$

Step 4

Solve for $t$ .

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Step 4.1

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

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Step 4.1.1

Subtract $49$ from both sides of the equation.

$- t = 42 - 49$

Step 4.1.2

Subtract $49$ from $42$ .

$- t = - 7$

Step 4.2

Divide each term in $- t = - 7$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- t = - 7$ by $- 1$ .

$\frac{- t}{- 1} = \frac{- 7}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{- 7}{- 1}$

Step 4.2.2.2

Divide $t$ by $1$ .

$t = \frac{- 7}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 7$ by $- 1$ .

$t = 7$