Basic Math Examples

$\frac{4 (t - 1)}{8} = \frac{2 (t + 3)}{8}$

Step 1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$4 (t - 1) = 2 (t + 3)$

Step 2

Simplify $4 (t - 1)$ .

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Step 2.1

Rewrite.

$0 + 0 + 4 (t - 1) = 2 (t + 3)$

Step 2.2

Simplify by adding zeros.

$4 (t - 1) = 2 (t + 3)$

Step 2.3

Apply the distributive property.

$4 t + 4 \cdot - 1 = 2 (t + 3)$

Step 2.4

Multiply $4$ by $- 1$ .

$4 t - 4 = 2 (t + 3)$

Step 3

Simplify $2 (t + 3)$ .

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Step 3.1

Apply the distributive property.

$4 t - 4 = 2 t + 2 \cdot 3$

Step 3.2

Multiply $2$ by $3$ .

$4 t - 4 = 2 t + 6$

Step 4

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

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Step 4.1

Subtract $2 t$ from both sides of the equation.

$4 t - 4 - 2 t = 6$

Step 4.2

Subtract $2 t$ from $4 t$ .

$2 t - 4 = 6$

Step 5

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

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Step 5.1

Add $4$ to both sides of the equation.

$2 t = 6 + 4$

Step 5.2

Add $6$ and $4$ .

$2 t = 10$

Step 6

Divide each term in $2 t = 10$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 t = 10$ by $2$ .

$\frac{2 t}{2} = \frac{10}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{10}{2}$

Step 6.2.1.2

Divide $t$ by $1$ .

$t = \frac{10}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $10$ by $2$ .

$t = 5$