Algebra Examples

$- \frac{1}{4} + \frac{3}{4} a = - (- \frac{7}{4} a - 1)$

Step 1

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

$- \frac{1}{4} + \frac{3 a}{4} = - (- \frac{7}{4} a - 1)$

Step 2

Simplify $- (- \frac{7}{4} a - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $a$ and $\frac{7}{4}$ .

$- \frac{1}{4} + \frac{3 a}{4} = - (- \frac{a \cdot 7}{4} - 1)$

Step 2.1.2

Move $7$ to the left of $a$ .

$- \frac{1}{4} + \frac{3 a}{4} = - (- \frac{7 a}{4} - 1)$

Step 2.2

Apply the distributive property.

$- \frac{1}{4} + \frac{3 a}{4} = - - \frac{7 a}{4} - - 1$

Step 2.3

Multiply $- - \frac{7 a}{4}$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$- \frac{1}{4} + \frac{3 a}{4} = 1 \frac{7 a}{4} - - 1$

Step 2.3.2

Multiply $\frac{7 a}{4}$ by $1$ .

$- \frac{1}{4} + \frac{3 a}{4} = \frac{7 a}{4} - - 1$

Step 2.4

Multiply $- 1$ by $- 1$ .

$- \frac{1}{4} + \frac{3 a}{4} = \frac{7 a}{4} + 1$

Step 3

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

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Step 3.1

Subtract $\frac{7 a}{4}$ from both sides of the equation.

$- \frac{1}{4} + \frac{3 a}{4} - \frac{7 a}{4} = 1$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 1 + 3 a - 7 a}{4} = 1$

Step 3.3

Subtract $7 a$ from $3 a$ .

$\frac{- 1 - 4 a}{4} = 1$

Step 3.4

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 (1) - 4 a}{4} = 1$

Step 3.5

Factor $- 1$ out of $- 4 a$ .

$\frac{- 1 (1) - (4 a)}{4} = 1$

Step 3.6

Factor $- 1$ out of $- 1 (1) - (4 a)$ .

$\frac{- 1 (1 + 4 a)}{4} = 1$

Step 3.7

Move the negative in front of the fraction.

$- \frac{1 + 4 a}{4} = 1$

Step 4

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{1 + 4 a}{4}) = - 4 \cdot 1$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 4 (- \frac{1 + 4 a}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{1 + 4 a}{4}$ into the numerator.

$- 4 \frac{- (1 + 4 a)}{4} = - 4 \cdot 1$

Step 5.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- (1 + 4 a)}{4} = - 4 \cdot 1$

Step 5.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- (1 + 4 a)}{4} = - 4 \cdot 1$

Step 5.1.1.1.4

Rewrite the expression.

$- - (1 + 4 a) = - 4 \cdot 1$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (1 + 4 a) = - 4 \cdot 1$

Step 5.1.1.2.2

Multiply $1 + 4 a$ by $1$ .

$1 + 4 a = - 4 \cdot 1$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 4$ by $1$ .

$1 + 4 a = - 4$

Step 6

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

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Step 6.1

Subtract $1$ from both sides of the equation.

$4 a = - 4 - 1$

Step 6.2

Subtract $1$ from $- 4$ .

$4 a = - 5$

Step 7

Divide each term in $4 a = - 5$ by $4$ and simplify.

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Step 7.1

Divide each term in $4 a = - 5$ by $4$ .

$\frac{4 a}{4} = \frac{- 5}{4}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $4$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{- 5}{4}$

Step 7.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 5}{4}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Move the negative in front of the fraction.

$a = - \frac{5}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{5}{4}$

Decimal Form:

$a = - 1.25$

Mixed Number Form:

$a = - 1 \frac{1}{4}$