Algebra Examples

\frac{1}{2} + \frac{2}{5} t - 1 = \frac{1}{5} t + t

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

Step 1

Since

t

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

\frac{1}{5} t + t = \frac{1}{2} + \frac{2}{5} t - 1

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

Step 2

Simplify

\frac{1}{5} t + t

$\frac{1}{5} t + t$ .

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Step 2.1

Combine

\frac{1}{5}

$\frac{1}{5}$ and

t

$t$ .

\frac{t}{5} + t = \frac{1}{2} + \frac{2}{5} t - 1

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

Step 2.2

To write

t

$t$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 2.3

Simplify terms.

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Step 2.3.1

Combine

t

$t$ and

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 2.3.2

Combine the numerators over the common denominator.

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

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

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

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

Step 2.4

Simplify the numerator.

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Step 2.4.1

Move

5

$5$ to the left of

t

$t$ .

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

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

Step 2.4.2

Add

t

$t$ and

5 t

$5 t$ .

\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1

$\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1$

\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1

$\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1$

\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1

$\frac{6 t}{5} = \frac{1}{2} + \frac{2}{5} t - 1$

Step 3

Simplify

\frac{1}{2} + \frac{2}{5} t - 1

$\frac{1}{2} + \frac{2}{5} t - 1$ .

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Step 3.1

Combine

\frac{2}{5}

$\frac{2}{5}$ and

t

$t$ .

\frac{6 t}{5} = \frac{1}{2} + \frac{2 t}{5} - 1

$\frac{6 t}{5} = \frac{1}{2} + \frac{2 t}{5} - 1$

Step 3.2

To write

- 1

$- 1$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{6 t}{5} = \frac{2 t}{5} + \frac{1}{2} - 1 \cdot \frac{2}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{1}{2} - 1 \cdot \frac{2}{2}$

Step 3.3

Combine

- 1

$- 1$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{6 t}{5} = \frac{2 t}{5} + \frac{1}{2} + \frac{- 1 \cdot 2}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{1}{2} + \frac{- 1 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

\frac{6 t}{5} = \frac{2 t}{5} + \frac{1 - 1 \cdot 2}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{1 - 1 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply

- 1

$- 1$ by

2

$2$ .

\frac{6 t}{5} = \frac{2 t}{5} + \frac{1 - 2}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{1 - 2}{2}$

Step 3.5.2

Subtract

2

$2$ from

1

$1$ .

\frac{6 t}{5} = \frac{2 t}{5} + \frac{- 1}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{- 1}{2}$

\frac{6 t}{5} = \frac{2 t}{5} + \frac{- 1}{2}

$\frac{6 t}{5} = \frac{2 t}{5} + \frac{- 1}{2}$

Step 3.6

Move the negative in front of the fraction.

\frac{6 t}{5} = \frac{2 t}{5} - \frac{1}{2}

$\frac{6 t}{5} = \frac{2 t}{5} - \frac{1}{2}$

\frac{6 t}{5} = \frac{2 t}{5} - \frac{1}{2}

$\frac{6 t}{5} = \frac{2 t}{5} - \frac{1}{2}$

Step 4

Move all terms containing

t

$t$ to the left side of the equation.

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Step 4.1

Subtract

\frac{2 t}{5}

$\frac{2 t}{5}$ from both sides of the equation.

\frac{6 t}{5} - \frac{2 t}{5} = - \frac{1}{2}

$\frac{6 t}{5} - \frac{2 t}{5} = - \frac{1}{2}$

Step 4.2

Combine the numerators over the common denominator.

\frac{6 t - 2 t}{5} = - \frac{1}{2}

$\frac{6 t - 2 t}{5} = - \frac{1}{2}$

Step 4.3

Subtract

2 t

$2 t$ from

6 t

$6 t$ .

\frac{4 t}{5} = - \frac{1}{2}

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

\frac{4 t}{5} = - \frac{1}{2}

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

Step 5

Multiply both sides of the equation by

\frac{5}{4}

$\frac{5}{4}$ .

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

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify

\frac{5}{4} \cdot \frac{4 t}{5}

$\frac{5}{4} \cdot \frac{4 t}{5}$ .

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Step 6.1.1.1

Cancel the common factor of

5

$5$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of

$4$ .

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Step 6.1.1.2.1

Factor

$4$ out of

$4 t$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply

$\frac{5}{4} (- \frac{1}{2})$ .

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Step 6.2.1.1

Multiply

$\frac{5}{4}$ by

$\frac{1}{2}$ .

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

Step 6.2.1.2

Multiply

$4$ by

$2$ .

$t = - \frac{5}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{5}{8}$

Decimal Form:

$t = - 0.625$