Basic Math Examples

$1.2 a - \frac{0.18 a - 0.05}{0.5} = 0.4 a + 8.9$

Step 1

Simplify $1.2 a - \frac{0.18 a - 0.05}{0.5}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $0.01$ out of $0.18 a - 0.05$ .

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Step 1.1.1.1

Factor $0.01$ out of $0.18 a$ .

$1.2 a - \frac{0.01 (18 a) - 0.05}{0.5} = 0.4 a + 8.9$

Step 1.1.1.2

Factor $0.01$ out of $- 0.05$ .

$1.2 a - \frac{0.01 (18 a) + 0.01 (- 5)}{0.5} = 0.4 a + 8.9$

Step 1.1.1.3

Factor $0.01$ out of $0.01 (18 a) + 0.01 (- 5)$ .

$1.2 a - \frac{0.01 (18 a - 5)}{0.5} = 0.4 a + 8.9$

Step 1.1.2

Factor $0.5$ out of $0.5$ .

$1.2 a - \frac{0.01 (18 a - 5)}{0.5 (1)} = 0.4 a + 8.9$

Step 1.1.3

Separate fractions.

$1.2 a - (\frac{0.01}{0.5} \cdot \frac{18 a - 5}{1}) = 0.4 a + 8.9$

Step 1.1.4

Divide $0.01$ by $0.5$ .

$1.2 a - (0.02 \frac{18 a - 5}{1}) = 0.4 a + 8.9$

Step 1.1.5

Cancel the common factor of $0.02$ .

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Step 1.1.5.1

Factor $0.02$ out of $1$ .

$1.2 a - (0.02 \frac{18 a - 5}{0.02 \cdot 50}) = 0.4 a + 8.9$

Step 1.1.5.2

Cancel the common factor.

$1.2 a - (0.02 \frac{18 a - 5}{0.02 \cdot 50}) = 0.4 a + 8.9$

Step 1.1.5.3

Rewrite the expression.

$1.2 a - \frac{18 a - 5}{50} = 0.4 a + 8.9$

Step 1.2

To write $1.2 a$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$1.2 a \cdot \frac{50}{50} - \frac{18 a - 5}{50} = 0.4 a + 8.9$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $1.2 a$ and $\frac{50}{50}$ .

$\frac{1.2 a \cdot 50}{50} - \frac{18 a - 5}{50} = 0.4 a + 8.9$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{1.2 a \cdot 50 - (18 a - 5)}{50} = 0.4 a + 8.9$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $0.2$ out of $1.2 a \cdot 50 - (18 a - 5)$ .

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Step 1.4.1.1

Move $a$ .

$\frac{1.2 \cdot 50 a - (18 a - 5)}{50} = 0.4 a + 8.9$

Step 1.4.1.2

Factor $0.2$ out of $1.2 \cdot 50 a$ .

$\frac{0.2 (6 \cdot 50 a) - (18 a - 5)}{50} = 0.4 a + 8.9$

Step 1.4.1.3

Factor $0.2$ out of $- (18 a - 5)$ .

$\frac{0.2 (6 \cdot 50 a) + 0.2 (- 5 (18 a - 5))}{50} = 0.4 a + 8.9$

Step 1.4.1.4

Factor $0.2$ out of $0.2 (6 \cdot 50 a) + 0.2 (- 5 (18 a - 5))$ .

$\frac{0.2 (6 \cdot 50 a - 5 (18 a - 5))}{50} = 0.4 a + 8.9$

Step 1.4.2

Factor $5$ out of $6 \cdot 50 a - 5 (18 a - 5)$ .

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Step 1.4.2.1

Factor $5$ out of $6 \cdot 50 a$ .

$\frac{0.2 (5 (6 \cdot 10 a) - 5 (18 a - 5))}{50} = 0.4 a + 8.9$

Step 1.4.2.2

Factor $5$ out of $- 5 (18 a - 5)$ .

$\frac{0.2 (5 (6 \cdot 10 a) + 5 (- (18 a - 5)))}{50} = 0.4 a + 8.9$

Step 1.4.2.3

Factor $5$ out of $5 (6 \cdot 10 a) + 5 (- (18 a - 5))$ .

$\frac{0.2 (5 (6 \cdot 10 a - (18 a - 5)))}{50} = 0.4 a + 8.9$

Step 1.4.3

Multiply $6$ by $10$ .

$\frac{0.2 (5 (60 a - (18 a - 5)))}{50} = 0.4 a + 8.9$

Step 1.4.4

Apply the distributive property.

$\frac{0.2 (5 (60 a - (18 a) - - 5))}{50} = 0.4 a + 8.9$

Step 1.4.5

Multiply $18$ by $- 1$ .

$\frac{0.2 (5 (60 a - 18 a - - 5))}{50} = 0.4 a + 8.9$

Step 1.4.6

Multiply $- 1$ by $- 5$ .

$\frac{0.2 (5 (60 a - 18 a + 5))}{50} = 0.4 a + 8.9$

Step 1.4.7

Subtract $18 a$ from $60 a$ .

$\frac{0.2 \cdot 5 (42 a + 5)}{50} = 0.4 a + 8.9$

Step 1.4.8

Combine exponents.

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Step 1.4.8.1

Multiply $0.2$ by $5$ .

$\frac{1 (42 a + 5)}{50} = 0.4 a + 8.9$

Step 1.4.8.2

Multiply $42 a + 5$ by $1$ .

$\frac{42 a + 5}{50} = 0.4 a + 8.9$

Step 2

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

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Step 2.1

Subtract $0.4 a$ from both sides of the equation.

$\frac{42 a + 5}{50} - 0.4 a = 8.9$

Step 2.2

To write $- 0.4 a$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$\frac{42 a + 5}{50} - 0.4 a \cdot \frac{50}{50} = 8.9$

Step 2.3

Combine $- 0.4 a$ and $\frac{50}{50}$ .

$\frac{42 a + 5}{50} + \frac{- 0.4 a \cdot 50}{50} = 8.9$

Step 2.4

Combine the numerators over the common denominator.

$\frac{42 a + 5 - 0.4 a \cdot 50}{50} = 8.9$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $50$ by $- 0.4$ .

$\frac{42 a + 5 - 20 a}{50} = 8.9$

Step 2.5.2

Subtract $20 a$ from $42 a$ .

$\frac{22 a + 5}{50} = 8.9$

Step 2.5.3

Factor $1$ out of $22 a + 5$ .

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Step 2.5.3.1

Factor $1$ out of $22 a$ .

$\frac{1 (22 a) + 5}{50} = 8.9$

Step 2.5.3.2

Rewrite $5$ as $1 (5)$ .

$\frac{1 (22 a) + 1 (5)}{50} = 8.9$

Step 2.5.3.3

Factor $1$ out of $1 (22 a) + 1 (5)$ .

$\frac{1 (22 a + 5)}{50} = 8.9$

Step 2.6

Multiply $22 a + 5$ by $1$ .

$\frac{22 a + 5}{50} = 8.9$

Step 3

Multiply both sides by $50$ .

$\frac{22 a + 5}{50} \cdot 50 = 8.9 \cdot 50$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $50$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{22 a + 5}{50} \cdot 50 = 8.9 \cdot 50$

Step 4.1.1.2

Rewrite the expression.

$22 a + 5 = 8.9 \cdot 50$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $8.9$ by $50$ .

$22 a + 5 = 445$

Step 5

Solve for $a$ .

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Step 5.1

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

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Step 5.1.1

Subtract $5$ from both sides of the equation.

$22 a = 445 - 5$

Step 5.1.2

Subtract $5$ from $445$ .

$22 a = 440$

Step 5.2

Divide each term in $22 a = 440$ by $22$ and simplify.

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Step 5.2.1

Divide each term in $22 a = 440$ by $22$ .

$\frac{22 a}{22} = \frac{440}{22}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $22$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{22 a}{22} = \frac{440}{22}$

Step 5.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{440}{22}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $440$ by $22$ .

$a = 20$