Precalculus Examples

$2 - 4 x + 5 (x - 1) < - 6 (x - 2)$

Step 1

Simplify $2 - 4 x + 5 (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 - 4 x + 5 x + 5 \cdot - 1 < - 6 (x - 2)$

Step 1.1.2

Multiply $5$ by $- 1$ .

$2 - 4 x + 5 x - 5 < - 6 (x - 2)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $5$ from $2$ .

$- 4 x + 5 x - 3 < - 6 (x - 2)$

Step 1.2.2

Add $- 4 x$ and $5 x$ .

$x - 3 < - 6 (x - 2)$

Step 2

Simplify $- 6 (x - 2)$ .

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Step 2.1

Apply the distributive property.

$x - 3 < - 6 x - 6 \cdot - 2$

Step 2.2

Multiply $- 6$ by $- 2$ .

$x - 3 < - 6 x + 12$

Step 3

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

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Step 3.1

Add $6 x$ to both sides of the inequality.

$x - 3 + 6 x < 12$

Step 3.2

Add $x$ and $6 x$ .

$7 x - 3 < 12$

Step 4

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

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Step 4.1

Add $3$ to both sides of the inequality.

$7 x < 12 + 3$

Step 4.2

Add $12$ and $3$ .

$7 x < 15$

Step 5

Divide each term in $7 x < 15$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x < 15$ by $7$ .

$\frac{7 x}{7} < \frac{15}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} < \frac{15}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{15}{7}$

Step 6

Convert the inequality to interval notation.

$(- \infty, \frac{15}{7})$

Step 7