Finite Math Examples

$\frac{3 x - 1}{- 34} > \frac{1}{2} x + 1$

Step 1

Multiply both sides by $- 34$ .

$\frac{3 x - 1}{- 34} \cdot - 34 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{3 x - 1}{- 34} \cdot - 34$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor of $34$ .

Tap for more steps...

Step 2.1.1.1.1

Factor $34$ out of $- 34$ .

$\frac{3 x - 1}{34 (- 1)} \cdot - 34 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.1.2

Factor $34$ out of $- 34$ .

$\frac{3 x - 1}{34 \cdot - 1} \cdot (34 \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{3 x - 1}{34 \cdot - 1} \cdot (34 \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{3 x - 1}{- 1} \cdot - 1 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.2

Combine $\frac{3 x - 1}{- 1}$ and $- 1$ .

$\frac{(3 x - 1) \cdot - 1}{- 1} < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.3

Simplify the expression.

Tap for more steps...

Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{(3 x - 1) \cdot - 1}{- 1}$ .

$- 1 \cdot ((3 x - 1) \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((3 x - 1) \cdot - 1)$ as $- ((3 x - 1) \cdot - 1)$ .

$- ((3 x - 1) \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.4

Apply the distributive property.

$- (3 x \cdot - 1 - 1 \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.5

Multiply.

Tap for more steps...

Step 2.1.1.5.1

Multiply $- 1$ by $3$ .

$- (- 3 x - 1 \cdot - 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.5.2

Multiply $- 1$ by $- 1$ .

$- (- 3 x + 1) < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.6

Apply the distributive property.

$- (- 3 x) - 1 \cdot 1 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.7

Multiply.

Tap for more steps...

Step 2.1.1.7.1

Multiply $- 3$ by $- 1$ .

$3 x - 1 \cdot 1 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.1.1.7.2

Multiply $- 1$ by $1$ .

$3 x - 1 < (\frac{1}{2} x + 1) \cdot - 34$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $(\frac{1}{2} x + 1) \cdot - 34$ .

Tap for more steps...

Step 2.2.1.1

Simplify terms.

Tap for more steps...

Step 2.2.1.1.1

Combine $\frac{1}{2}$ and $x$ .

$3 x - 1 < (\frac{x}{2} + 1) \cdot - 34$

Step 2.2.1.1.2

Apply the distributive property.

$3 x - 1 < \frac{x}{2} \cdot - 34 + 1 \cdot - 34$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.3.1

Factor $2$ out of $- 34$ .

$3 x - 1 < \frac{x}{2} \cdot (2 (- 17)) + 1 \cdot - 34$

Step 2.2.1.1.3.2

Cancel the common factor.

$3 x - 1 < \frac{x}{2} \cdot (2 \cdot - 17) + 1 \cdot - 34$

Step 2.2.1.1.3.3

Rewrite the expression.

$3 x - 1 < x \cdot - 17 + 1 \cdot - 34$

Step 2.2.1.1.4

Multiply $- 34$ by $1$ .

$3 x - 1 < x \cdot - 17 - 34$

Step 2.2.1.2

Move $- 17$ to the left of $x$ .

$3 x - 1 < - 17 x - 34$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $17 x$ to both sides of the inequality.

$3 x - 1 + 17 x < - 34$

Step 3.1.2

Add $3 x$ and $17 x$ .

$20 x - 1 < - 34$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $1$ to both sides of the inequality.

$20 x < - 34 + 1$

Step 3.2.2

Add $- 34$ and $1$ .

$20 x < - 33$

Step 3.3

Divide each term in $20 x < - 33$ by $20$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $20 x < - 33$ by $20$ .

$\frac{20 x}{20} < \frac{- 33}{20}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $20$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{20 x}{20} < \frac{- 33}{20}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 33}{20}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Move the negative in front of the fraction.

$x < - \frac{33}{20}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{33}{20}$

Interval Notation:

$(- \infty, - \frac{33}{20})$