Pre-Algebra Examples

$- 8 r - 6 = - 4 - 7 r + 3 r$

Step 1

Since $r$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 4 - 7 r + 3 r = - 8 r - 6$

Step 2

Add $- 7 r$ and $3 r$ .

$- 4 - 4 r = - 8 r - 6$

Step 3

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

Tap for more steps...

Step 3.1

Add $8 r$ to both sides of the equation.

$- 4 - 4 r + 8 r = - 6$

Step 3.2

Add $- 4 r$ and $8 r$ .

$- 4 + 4 r = - 6$

Step 4

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

Tap for more steps...

Step 4.1

Add $4$ to both sides of the equation.

$4 r = - 6 + 4$

Step 4.2

Add $- 6$ and $4$ .

$4 r = - 2$

Step 5

Divide each term in $4 r = - 2$ by $4$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $4 r = - 2$ by $4$ .

$\frac{4 r}{4} = \frac{- 2}{4}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{4 r}{4} = \frac{- 2}{4}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 2}{4}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Cancel the common factor of $- 2$ and $4$ .

Tap for more steps...

Step 5.3.1.1

Factor $2$ out of $- 2$ .

$r = \frac{2 (- 1)}{4}$

Step 5.3.1.2

Cancel the common factors.

Tap for more steps...

Step 5.3.1.2.1

Factor $2$ out of $4$ .

$r = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$r = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$r = \frac{- 1}{2}$

Step 5.3.2

Move the negative in front of the fraction.

$r = - \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{1}{2}$

Decimal Form:

$r = - 0.5$