Basic Math Examples

$5 - \frac{3 a - 4}{5} = \frac{7 - 2 a}{2}$

Step 1

Multiply both sides by $2$ .

$(5 - \frac{3 a - 4}{5}) \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(5 - \frac{3 a - 4}{5}) \cdot 2$ .

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Step 2.1.1.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(5 \cdot \frac{5}{5} - \frac{3 a - 4}{5}) \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

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

$(\frac{5 \cdot 5}{5} - \frac{3 a - 4}{5}) \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - (3 a - 4)}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Multiply $5$ by $5$ .

$\frac{25 - (3 a - 4)}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.3.2

Apply the distributive property.

$\frac{25 - (3 a) - - 4}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.3.3

Multiply $3$ by $- 1$ .

$\frac{25 - 3 a - - 4}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.3.4

Multiply $- 1$ by $- 4$ .

$\frac{25 - 3 a + 4}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.3.5

Add $25$ and $4$ .

$\frac{- 3 a + 29}{5} \cdot 2 = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4

Simplify terms.

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Step 2.1.1.4.1

Combine $\frac{- 3 a + 29}{5}$ and $2$ .

$\frac{(- 3 a + 29) \cdot 2}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.2

Move $2$ to the left of $- 3 a + 29$ .

$\frac{2 \cdot (- 3 a + 29)}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.3

Factor $- 1$ out of $- 3 a$ .

$\frac{2 (- (3 a) + 29)}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.4

Rewrite $29$ as $- 1 (- 29)$ .

$\frac{2 (- (3 a) - 1 (- 29))}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.5

Factor $- 1$ out of $- (3 a) - 1 (- 29)$ .

$\frac{2 (- (3 a - 29))}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.6

Simplify the expression.

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Step 2.1.1.4.6.1

Rewrite $- (3 a - 29)$ as $- 1 (3 a - 29)$ .

$\frac{2 (- 1 (3 a - 29))}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.1.1.4.6.2

Move the negative in front of the fraction.

$- \frac{2 (3 a - 29)}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{7 - 2 a}{2} \cdot 2$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$- \frac{2 (3 a - 29)}{5} = \frac{7 - 2 a}{2} \cdot 2$

Step 2.2.1.1.2

Rewrite the expression.

$- \frac{2 (3 a - 29)}{5} = 7 - 2 a$

Step 2.2.1.2

Reorder $7$ and $- 2 a$ .

$- \frac{2 (3 a - 29)}{5} = - 2 a + 7$

Step 3

Solve for $a$ .

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Step 3.1

Multiply both sides by $5$ .

$- \frac{2 (3 a - 29)}{5} \cdot 5 = (- 2 a + 7) \cdot 5$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $- \frac{2 (3 a - 29)}{5} \cdot 5$ .

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Step 3.2.1.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1.1

Move the leading negative in $- \frac{2 (3 a - 29)}{5}$ into the numerator.

$\frac{- 2 (3 a - 29)}{5} \cdot 5 = (- 2 a + 7) \cdot 5$

Step 3.2.1.1.1.2

Cancel the common factor.

$\frac{- 2 (3 a - 29)}{5} \cdot 5 = (- 2 a + 7) \cdot 5$

Step 3.2.1.1.1.3

Rewrite the expression.

$- 2 (3 a - 29) = (- 2 a + 7) \cdot 5$

Step 3.2.1.1.2

Apply the distributive property.

$- 2 (3 a) - 2 \cdot - 29 = (- 2 a + 7) \cdot 5$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $3$ by $- 2$ .

$- 6 a - 2 \cdot - 29 = (- 2 a + 7) \cdot 5$

Step 3.2.1.1.3.2

Multiply $- 2$ by $- 29$ .

$- 6 a + 58 = (- 2 a + 7) \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(- 2 a + 7) \cdot 5$ .

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Step 3.2.2.1.1

Apply the distributive property.

$- 6 a + 58 = - 2 a \cdot 5 + 7 \cdot 5$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $5$ by $- 2$ .

$- 6 a + 58 = - 10 a + 7 \cdot 5$

Step 3.2.2.1.2.2

Multiply $7$ by $5$ .

$- 6 a + 58 = - 10 a + 35$

Step 3.3

Solve for $a$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $10 a$ to both sides of the equation.

$- 6 a + 58 + 10 a = 35$

Step 3.3.1.2

Add $- 6 a$ and $10 a$ .

$4 a + 58 = 35$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $58$ from both sides of the equation.

$4 a = 35 - 58$

Step 3.3.2.2

Subtract $58$ from $35$ .

$4 a = - 23$

Step 3.3.3

Divide each term in $4 a = - 23$ by $4$ and simplify.

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Step 3.3.3.1

Divide each term in $4 a = - 23$ by $4$ .

$\frac{4 a}{4} = \frac{- 23}{4}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $4$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{- 23}{4}$

Step 3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 23}{4}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Move the negative in front of the fraction.

$a = - \frac{23}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{23}{4}$

Decimal Form:

$a = - 5.75$

Mixed Number Form:

$a = - 5 \frac{3}{4}$