Algebra Examples

$8 r - (5 r + 4) \geq - 31$

Step 1

Simplify $8 r - (5 r + 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 r - (5 r) - 1 \cdot 4 \geq - 31$

Step 1.1.2

Multiply $5$ by $- 1$ .

$8 r - 5 r - 1 \cdot 4 \geq - 31$

Step 1.1.3

Multiply $- 1$ by $4$ .

$8 r - 5 r - 4 \geq - 31$

Step 1.2

Subtract $5 r$ from $8 r$ .

$3 r - 4 \geq - 31$

Step 2

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

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Step 2.1

Add $4$ to both sides of the inequality.

$3 r \geq - 31 + 4$

Step 2.2

Add $- 31$ and $4$ .

$3 r \geq - 27$

Step 3

Divide each term in $3 r \geq - 27$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 r \geq - 27$ by $3$ .

$\frac{3 r}{3} \geq \frac{- 27}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 r}{3} \geq \frac{- 27}{3}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r \geq \frac{- 27}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 27$ by $3$ .

$r \geq - 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$r \geq - 9$

Interval Notation:

$[- 9, \infty)$