Finite Math Examples

$35 (x - 5) + 23 (x - 3) > - 6$

Step 1

Simplify $35 (x - 5) + 23 (x - 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$35 x + 35 \cdot - 5 + 23 (x - 3) > - 6$

Step 1.1.2

Multiply $35$ by $- 5$ .

$35 x - 175 + 23 (x - 3) > - 6$

Step 1.1.3

Apply the distributive property.

$35 x - 175 + 23 x + 23 \cdot - 3 > - 6$

Step 1.1.4

Multiply $23$ by $- 3$ .

$35 x - 175 + 23 x - 69 > - 6$

$35 x - 175 + 23 x - 69 > - 6$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $35 x$ and $23 x$ .

$58 x - 175 - 69 > - 6$

Step 1.2.2

Subtract $69$ from $- 175$ .

$58 x - 244 > - 6$

$58 x - 244 > - 6$

$58 x - 244 > - 6$

Step 2

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

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Step 2.1

Add $244$ to both sides of the inequality.

$58 x > - 6 + 244$

Step 2.2

Add $- 6$ and $244$ .

$58 x > 238$

$58 x > 238$

Step 3

Divide each term in $58 x > 238$ by $58$ and simplify.

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Step 3.1

Divide each term in $58 x > 238$ by $58$ .

$\frac{58 x}{58} > \frac{238}{58}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $58$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{58 x}{58} > \frac{238}{58}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{238}{58}$

$x > \frac{238}{58}$

$x > \frac{238}{58}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $238$ and $58$ .

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Step 3.3.1.1

Factor $2$ out of $238$ .

$x > \frac{2 (119)}{58}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $58$ .

$x > \frac{2 \cdot 119}{2 \cdot 29}$

Step 3.3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot 119}{2 \cdot 29}$

Step 3.3.1.2.3

Rewrite the expression.

$x > \frac{119}{29}$

$x > \frac{119}{29}$

$x > \frac{119}{29}$

$x > \frac{119}{29}$

$x > \frac{119}{29}$

Step 4

Convert the inequality to interval notation.

$(\frac{119}{29}, \infty)$

Step 5

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