Finite Math Examples

$\frac{6 - x}{4} < \frac{3 x - 4}{2}$

Step 1

Multiply both sides by $4$ .

$\frac{6 - x}{4} \cdot 4 < \frac{3 x - 4}{2} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{6 - x}{4} \cdot 4$ .

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Step 2.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{6 - x}{4} \cdot 4 < \frac{3 x - 4}{2} \cdot 4$

Step 2.1.1.1.2

Rewrite the expression.

$6 - x < \frac{3 x - 4}{2} \cdot 4$

Step 2.1.1.2

Reorder $6$ and $- x$ .

$- x + 6 < \frac{3 x - 4}{2} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3 x - 4}{2} \cdot 4$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $4$ .

$- x + 6 < \frac{3 x - 4}{2} \cdot (2 (2))$

Step 2.2.1.1.2

Cancel the common factor.

$- x + 6 < \frac{3 x - 4}{2} \cdot (2 \cdot 2)$

Step 2.2.1.1.3

Rewrite the expression.

$- x + 6 < (3 x - 4) \cdot 2$

Step 2.2.1.2

Apply the distributive property.

$- x + 6 < 3 x \cdot 2 - 4 \cdot 2$

Step 2.2.1.3

Multiply.

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Step 2.2.1.3.1

Multiply $2$ by $3$ .

$- x + 6 < 6 x - 4 \cdot 2$

Step 2.2.1.3.2

Multiply $- 4$ by $2$ .

$- x + 6 < 6 x - 8$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6 x$ from both sides of the inequality.

$- x + 6 - 6 x < - 8$

Step 3.1.2

Subtract $6 x$ from $- x$ .

$- 7 x + 6 < - 8$

Step 3.2

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

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Step 3.2.1

Subtract $6$ from both sides of the inequality.

$- 7 x < - 8 - 6$

Step 3.2.2

Subtract $6$ from $- 8$ .

$- 7 x < - 14$

Step 3.3

Divide each term in $- 7 x < - 14$ by $- 7$ and simplify.

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Step 3.3.1

Divide each term in $- 7 x < - 14$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} > \frac{- 14}{- 7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} > \frac{- 14}{- 7}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 14}{- 7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 14$ by $- 7$ .

$x > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$