Algebra Examples

$- \frac{3}{4} (16 x + 8) = 19 - (10 x - 3)$

Step 1

Simplify $- \frac{3}{4} \cdot (16 x + 8)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{3}{4} \cdot (16 x + 8) = 19 - (10 x - 3)$

Step 1.2

Simplify by adding zeros.

$- \frac{3}{4} \cdot (16 x + 8) = 19 - (10 x - 3)$

Step 1.3

Apply the distributive property.

$- \frac{3}{4} (16 x) - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

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

$\frac{- 3}{4} (16 x) - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.4.2

Factor $4$ out of $16 x$ .

$\frac{- 3}{4} (4 (4 x)) - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.4.3

Cancel the common factor.

$\frac{- 3}{4} (4 (4 x)) - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.4.4

Rewrite the expression.

$- 3 (4 x) - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.5

Multiply $4$ by $- 3$ .

$- 12 x - \frac{3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

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

$- 12 x + \frac{- 3}{4} \cdot 8 = 19 - (10 x - 3)$

Step 1.6.2

Factor $4$ out of $8$ .

$- 12 x + \frac{- 3}{4} \cdot (4 (2)) = 19 - (10 x - 3)$

Step 1.6.3

Cancel the common factor.

$- 12 x + \frac{- 3}{4} \cdot (4 \cdot 2) = 19 - (10 x - 3)$

Step 1.6.4

Rewrite the expression.

$- 12 x - 3 \cdot 2 = 19 - (10 x - 3)$

Step 1.7

Multiply $- 3$ by $2$ .

$- 12 x - 6 = 19 - (10 x - 3)$

Step 2

Simplify $19 - (10 x - 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 12 x - 6 = 19 - (10 x) - - 3$

Step 2.1.2

Multiply $10$ by $- 1$ .

$- 12 x - 6 = 19 - 10 x - - 3$

Step 2.1.3

Multiply $- 1$ by $- 3$ .

$- 12 x - 6 = 19 - 10 x + 3$

Step 2.2

Add $19$ and $3$ .

$- 12 x - 6 = - 10 x + 22$

Step 3

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

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Step 3.1

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

$- 12 x - 6 + 10 x = 22$

Step 3.2

Add $- 12 x$ and $10 x$ .

$- 2 x - 6 = 22$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$- 2 x = 22 + 6$

Step 4.2

Add $22$ and $6$ .

$- 2 x = 28$

Step 5

Divide each term in $- 2 x = 28$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 x = 28$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{28}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{28}{- 2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $28$ by $- 2$ .

$x = - 14$