Algebra Examples

$- \frac{4}{3} (12 v - 18) + 32 = - 8 (7 + 2 v)$

Step 1

Simplify $- \frac{4}{3} \cdot (12 v - 18) + 32$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- \frac{4}{3} (12 v) - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (12 v) - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.2.2

Factor $3$ out of $12 v$ .

$\frac{- 4}{3} (3 (4 v)) - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.2.3

Cancel the common factor.

$\frac{- 4}{3} (3 (4 v)) - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.2.4

Rewrite the expression.

$- 4 (4 v) - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.3

Multiply $4$ by $- 4$ .

$- 16 v - \frac{4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$- 16 v + \frac{- 4}{3} \cdot - 18 + 32 = - 8 (7 + 2 v)$

Step 1.1.4.2

Factor $3$ out of $- 18$ .

$- 16 v + \frac{- 4}{3} \cdot (3 (- 6)) + 32 = - 8 (7 + 2 v)$

Step 1.1.4.3

Cancel the common factor.

$- 16 v + \frac{- 4}{3} \cdot (3 \cdot - 6) + 32 = - 8 (7 + 2 v)$

Step 1.1.4.4

Rewrite the expression.

$- 16 v - 4 \cdot - 6 + 32 = - 8 (7 + 2 v)$

Step 1.1.5

Multiply $- 4$ by $- 6$ .

$- 16 v + 24 + 32 = - 8 (7 + 2 v)$

Step 1.2

Add $24$ and $32$ .

$- 16 v + 56 = - 8 (7 + 2 v)$

Step 2

Simplify $- 8 (7 + 2 v)$ .

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Step 2.1

Apply the distributive property.

$- 16 v + 56 = - 8 \cdot 7 - 8 (2 v)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 8$ by $7$ .

$- 16 v + 56 = - 56 - 8 (2 v)$

Step 2.2.2

Multiply $2$ by $- 8$ .

$- 16 v + 56 = - 56 - 16 v$

Step 3

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

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Step 3.1

Add $16 v$ to both sides of the equation.

$- 16 v + 56 + 16 v = - 56$

Step 3.2

Combine the opposite terms in $- 16 v + 56 + 16 v$ .

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Step 3.2.1

Add $- 16 v$ and $16 v$ .

$0 + 56 = - 56$

Step 3.2.2

Add $0$ and $56$ .

$56 = - 56$

Step 4

Since $56 \neq - 56$ , there are no solutions.

No solution