Algebra Examples

$4 (x - 3) - r + 2 x = 5 (3 x - 7) - 9 x$

Step 1

Simplify $4 (x - 3) - r + 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 x + 4 \cdot - 3 - r + 2 x = 5 (3 x - 7) - 9 x$

Step 1.1.2

Multiply $4$ by $- 3$ .

$4 x - 12 - r + 2 x = 5 (3 x - 7) - 9 x$

Step 1.2

Add $4 x$ and $2 x$ .

$6 x - 12 - r = 5 (3 x - 7) - 9 x$

Step 2

Simplify $5 (3 x - 7) - 9 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 x - 12 - r = 5 (3 x) + 5 \cdot - 7 - 9 x$

Step 2.1.2

Multiply $3$ by $5$ .

$6 x - 12 - r = 15 x + 5 \cdot - 7 - 9 x$

Step 2.1.3

Multiply $5$ by $- 7$ .

$6 x - 12 - r = 15 x - 35 - 9 x$

Step 2.2

Subtract $9 x$ from $15 x$ .

$6 x - 12 - r = 6 x - 35$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the equation.

$- 12 - r = 6 x - 35 - 6 x$

Step 3.2

Add $12$ to both sides of the equation.

$- r = 6 x - 35 - 6 x + 12$

Step 3.3

Combine the opposite terms in $6 x - 35 - 6 x + 12$ .

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Step 3.3.1

Subtract $6 x$ from $6 x$ .

$- r = 0 - 35 + 12$

Step 3.3.2

Subtract $35$ from $0$ .

$- r = - 35 + 12$

Step 3.4

Add $- 35$ and $12$ .

$- r = - 23$

Step 4

Divide each term in $- r = - 23$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- r = - 23$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 23}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 23}{- 1}$

Step 4.2.2

Divide $r$ by $1$ .

$r = \frac{- 23}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 23$ by $- 1$ .

$r = 23$