Algebra Examples

$3 (x - 4) \geq 5 x + 2$

Step 1

Simplify $3 (x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (x - 4) \geq 5 x + 2$

Step 1.2

Simplify by adding zeros.

$3 (x - 4) \geq 5 x + 2$

Step 1.3

Apply the distributive property.

$3 x + 3 \cdot - 4 \geq 5 x + 2$

Step 1.4

Multiply $3$ by $- 4$ .

$3 x - 12 \geq 5 x + 2$

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.

$3 x - 12 - 5 x \geq 2$

Step 2.2

Subtract $5 x$ from $3 x$ .

$- 2 x - 12 \geq 2$

Step 3

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

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Step 3.1

Add $12$ to both sides of the inequality.

$- 2 x \geq 2 + 12$

Step 3.2

Add $2$ and $12$ .

$- 2 x \geq 14$

Step 4

Divide each term in $- 2 x \geq 14$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x \geq 14$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{14}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{14}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{14}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $14$ by $- 2$ .

$x \leq - 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 7$

Interval Notation:

$(- \infty, - 7]$