Algebra Examples

$0.5 (9 v - 4) + 2 = 6 (0.25 v + 2)$

Step 1

Simplify $0.5 (9 v - 4) + 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$0.5 (9 v) + 0.5 \cdot - 4 + 2 = 6 (0.25 v + 2)$

Step 1.1.2

Multiply $9$ by $0.5$ .

$4.5 v + 0.5 \cdot - 4 + 2 = 6 (0.25 v + 2)$

Step 1.1.3

Multiply $0.5$ by $- 4$ .

$4.5 v - 2 + 2 = 6 (0.25 v + 2)$

$4.5 v - 2 + 2 = 6 (0.25 v + 2)$

Step 1.2

Simplify by adding numbers.

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Step 1.2.1

Add $- 2$ and $2$ .

$4.5 v + 0 = 6 (0.25 v + 2)$

Step 1.2.2

Add $4.5 v$ and $0$ .

$4.5 v = 6 (0.25 v + 2)$

$4.5 v = 6 (0.25 v + 2)$

$4.5 v = 6 (0.25 v + 2)$

Step 2

Simplify $6 (0.25 v + 2)$ .

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Step 2.1

Apply the distributive property.

$4.5 v = 6 (0.25 v) + 6 \cdot 2$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $0.25$ by $6$ .

$4.5 v = 1.5 v + 6 \cdot 2$

Step 2.2.2

Multiply $6$ by $2$ .

$4.5 v = 1.5 v + 12$

$4.5 v = 1.5 v + 12$

$4.5 v = 1.5 v + 12$

Step 3

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

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Step 3.1

Subtract $1.5 v$ from both sides of the equation.

$4.5 v - 1.5 v = 12$

Step 3.2

Subtract $1.5 v$ from $4.5 v$ .

$3 v = 12$

$3 v = 12$

Step 4

Divide each term in $3 v = 12$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 v = 12$ by $3$ .

$\frac{3 v}{3} = \frac{12}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 v}{3} = \frac{12}{3}$

Step 4.2.1.2

Divide $v$ by $1$ .

$v = \frac{12}{3}$

$v = \frac{12}{3}$

$v = \frac{12}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $12$ by $3$ .

$v = 4$

$v = 4$

$v = 4$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$