Algebra Examples

$0.5 (2 q + 1) = 0.75 q$

Step 1

Simplify $0.5 (2 q + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 0.5 (2 q + 1) = 0.75 q$

Step 1.2

Simplify by adding zeros.

$0.5 (2 q + 1) = 0.75 q$

Step 1.3

Apply the distributive property.

$0.5 (2 q) + 0.5 \cdot 1 = 0.75 q$

Step 1.4

Multiply $0.5 (2 q)$ .

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Step 1.4.1

Multiply $2$ by $0.5$ .

$1 q + 0.5 \cdot 1 = 0.75 q$

Step 1.4.2

Multiply $q$ by $1$ .

$q + 0.5 \cdot 1 = 0.75 q$

Step 1.5

Multiply $0.5$ by $1$ .

$q + 0.5 = 0.75 q$

Step 2

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

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Step 2.1

Subtract $0.75 q$ from both sides of the equation.

$q + 0.5 - 0.75 q = 0$

Step 2.2

Subtract $0.75 q$ from $q$ .

$0.25 q + 0.5 = 0$

Step 3

Subtract $0.5$ from both sides of the equation.

$0.25 q = - 0.5$

Step 4

Divide each term in $0.25 q = - 0.5$ by $0.25$ and simplify.

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Step 4.1

Divide each term in $0.25 q = - 0.5$ by $0.25$ .

$\frac{0.25 q}{0.25} = \frac{- 0.5}{0.25}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.25$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.25 q}{0.25} = \frac{- 0.5}{0.25}$

Step 4.2.1.2

Divide $q$ by $1$ .

$q = \frac{- 0.5}{0.25}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 0.5$ by $0.25$ .

$q = - 2$