Algebra Examples

$2 (4 + 2 x) \geq 5 x + 5$

Step 1

Simplify $2 (4 + 2 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (4 + 2 x) \geq 5 x + 5$

Step 1.2

Simplify by adding zeros.

$2 (4 + 2 x) \geq 5 x + 5$

Step 1.3

Apply the distributive property.

$2 \cdot 4 + 2 (2 x) \geq 5 x + 5$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $4$ .

$8 + 2 (2 x) \geq 5 x + 5$

Step 1.4.2

Multiply $2$ by $2$ .

$8 + 4 x \geq 5 x + 5$

Step 2

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

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Step 2.1

Subtract $5 x$ from both sides of the inequality.

$8 + 4 x - 5 x \geq 5$

Step 2.2

Subtract $5 x$ from $4 x$ .

$8 - x \geq 5$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the inequality.

$- x \geq 5 - 8$

Step 3.2

Subtract $8$ from $5$ .

$- x \geq - 3$

Step 4

Divide each term in $- x \geq - 3$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x \geq - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- 3}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- 3}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x \leq \frac{- 3}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 3$ by $- 1$ .

$x \leq 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$