Finite Math Examples

7 x - 14 \leq 4 x - 15

$7 x - 14 \leq 4 x - 15$

Step 1

Move all terms containing

x

$x$ to the left side of the inequality.

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Step 1.1

Subtract

4 x

$4 x$ from both sides of the inequality.

7 x - 14 - 4 x \leq - 15

$7 x - 14 - 4 x \leq - 15$

Step 1.2

Subtract

4 x

$4 x$ from

7 x

$7 x$ .

3 x - 14 \leq - 15

$3 x - 14 \leq - 15$

3 x - 14 \leq - 15

$3 x - 14 \leq - 15$

Step 2

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 2.1

Add

14

$14$ to both sides of the inequality.

3 x \leq - 15 + 14

$3 x \leq - 15 + 14$

Step 2.2

Add

- 15

$- 15$ and

14

$14$ .

3 x \leq - 1

$3 x \leq - 1$

3 x \leq - 1

$3 x \leq - 1$

Step 3

Divide each term in

3 x \leq - 1

$3 x \leq - 1$ by

3

$3$ and simplify.

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Step 3.1

Divide each term in

3 x \leq - 1

$3 x \leq - 1$ by

3

$3$ .

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

3

$3$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide

$x$ by

$1$ .

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

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

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

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

Step 4

Convert the inequality to interval notation.

$(- \infty, - \frac{1}{3}]$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$