Algebra Examples

$- \frac{4}{3} t + \frac{1}{2} = \frac{3}{2} - 2 t + \frac{5}{3} t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{3}{2} - 2 t + \frac{5}{3} t = - \frac{4}{3} t + \frac{1}{2}$

Step 2

Simplify $\frac{3}{2} - 2 t + \frac{5}{3} t$ .

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Step 2.1

Combine $\frac{5}{3}$ and $t$ .

$\frac{3}{2} - 2 t + \frac{5 t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.2

To write $- 2 t$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{2} - 2 t \cdot \frac{3}{3} + \frac{5 t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $- 2 t$ and $\frac{3}{3}$ .

$\frac{3}{2} + \frac{- 2 t \cdot 3}{3} + \frac{5 t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{3}{2} + \frac{- 2 t \cdot 3 + 5 t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $t$ out of $- 2 t \cdot 3 + 5 t$ .

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Step 2.4.1.1.1

Factor $t$ out of $- 2 t \cdot 3$ .

$\frac{3}{2} + \frac{t (- 2 \cdot 3) + 5 t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.1.1.2

Factor $t$ out of $5 t$ .

$\frac{3}{2} + \frac{t (- 2 \cdot 3) + t \cdot 5}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.1.1.3

Factor $t$ out of $t (- 2 \cdot 3) + t \cdot 5$ .

$\frac{3}{2} + \frac{t (- 2 \cdot 3 + 5)}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.1.2

Multiply $- 2$ by $3$ .

$\frac{3}{2} + \frac{t (- 6 + 5)}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.1.3

Add $- 6$ and $5$ .

$\frac{3}{2} + \frac{t \cdot - 1}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.2

Move $- 1$ to the left of $t$ .

$\frac{3}{2} + \frac{- 1 \cdot t}{3} = - \frac{4}{3} t + \frac{1}{2}$

Step 2.4.3

Move the negative in front of the fraction.

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

Step 3

Simplify each term.

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Step 3.1

Combine $t$ and $\frac{4}{3}$ .

$\frac{3}{2} - \frac{t}{3} = - \frac{t \cdot 4}{3} + \frac{1}{2}$

Step 3.2

Move $4$ to the left of $t$ .

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

Step 4

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

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Step 4.1

Add $\frac{4 t}{3}$ to both sides of the equation.

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 4.3

Add $- t$ and $4 t$ .

$\frac{3}{2} + \frac{3 t}{3} = \frac{1}{2}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Cancel the common factor.

$\frac{3}{2} + \frac{3 t}{3} = \frac{1}{2}$

Step 4.4.2

Divide $t$ by $1$ .

$\frac{3}{2} + t = \frac{1}{2}$

Step 5

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

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Step 5.1

Subtract $\frac{3}{2}$ from both sides of the equation.

$t = \frac{1}{2} - \frac{3}{2}$

Step 5.2

Combine the numerators over the common denominator.

$t = \frac{1 - 3}{2}$

Step 5.3

Subtract $3$ from $1$ .

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

Step 5.4

Divide $- 2$ by $2$ .

$t = - 1$