Finite Math Examples

$\frac{2 x - 3}{4} + x = \frac{2 x + 3}{2} + 9$

Step 1

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

Tap for more steps...

Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x - 3}{4} + x \cdot \frac{4}{4} = \frac{2 x + 3}{2} + 9$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Combine $x$ and $\frac{4}{4}$ .

$\frac{2 x - 3}{4} + \frac{x \cdot 4}{4} = \frac{2 x + 3}{2} + 9$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2 x - 3 + x \cdot 4}{4} = \frac{2 x + 3}{2} + 9$

Step 1.3

Simplify the numerator.

Tap for more steps...

Step 1.3.1

Add $2 x$ and $x \cdot 4$ .

Tap for more steps...

Step 1.3.1.1

Reorder $x$ and $4$ .

$\frac{2 x + 4 \cdot x - 3}{4} = \frac{2 x + 3}{2} + 9$

Step 1.3.1.2

Add $2 x$ and $4 \cdot x$ .

$\frac{6 x - 3}{4} = \frac{2 x + 3}{2} + 9$

Step 1.3.2

Factor $3$ out of $6 x - 3$ .

Tap for more steps...

Step 1.3.2.1

Factor $3$ out of $6 x$ .

$\frac{3 (2 x) - 3}{4} = \frac{2 x + 3}{2} + 9$

Step 1.3.2.2

Factor $3$ out of $- 3$ .

$\frac{3 (2 x) + 3 (- 1)}{4} = \frac{2 x + 3}{2} + 9$

Step 1.3.2.3

Factor $3$ out of $3 (2 x) + 3 (- 1)$ .

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 3}{2} + 9$

Step 2

Simplify $\frac{2 x + 3}{2} + 9$ .

Tap for more steps...

Step 2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 3}{2} + 9 \cdot \frac{2}{2}$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine $9$ and $\frac{2}{2}$ .

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 3}{2} + \frac{9 \cdot 2}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 3 + 9 \cdot 2}{2}$

Step 2.3

Simplify the numerator.

Tap for more steps...

Step 2.3.1

Multiply $9$ by $2$ .

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 3 + 18}{2}$

Step 2.3.2

Add $3$ and $18$ .

$\frac{3 (2 x - 1)}{4} = \frac{2 x + 21}{2}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{2 x + 21}{2}$ from both sides of the equation.

$\frac{3 (2 x - 1)}{4} - \frac{2 x + 21}{2} = 0$

Step 3.2

To write $- \frac{2 x + 21}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 (2 x - 1)}{4} - \frac{2 x + 21}{2} \cdot \frac{2}{2} = 0$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{2 x + 21}{2}$ by $\frac{2}{2}$ .

$\frac{3 (2 x - 1)}{4} - \frac{(2 x + 21) \cdot 2}{2 \cdot 2} = 0$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{3 (2 x - 1)}{4} - \frac{(2 x + 21) \cdot 2}{4} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 (2 x - 1) - (2 x + 21) \cdot 2}{4} = 0$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Apply the distributive property.

$\frac{3 (2 x) + 3 \cdot - 1 - (2 x + 21) \cdot 2}{4} = 0$

Step 3.5.2

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot - 1 - (2 x + 21) \cdot 2}{4} = 0$

Step 3.5.3

Multiply $3$ by $- 1$ .

$\frac{6 x - 3 - (2 x + 21) \cdot 2}{4} = 0$

Step 3.5.4

Apply the distributive property.

$\frac{6 x - 3 + (- (2 x) - 1 \cdot 21) \cdot 2}{4} = 0$

Step 3.5.5

Multiply $2$ by $- 1$ .

$\frac{6 x - 3 + (- 2 x - 1 \cdot 21) \cdot 2}{4} = 0$

Step 3.5.6

Multiply $- 1$ by $21$ .

$\frac{6 x - 3 + (- 2 x - 21) \cdot 2}{4} = 0$

Step 3.5.7

Apply the distributive property.

$\frac{6 x - 3 - 2 x \cdot 2 - 21 \cdot 2}{4} = 0$

Step 3.5.8

Multiply $2$ by $- 2$ .

$\frac{6 x - 3 - 4 x - 21 \cdot 2}{4} = 0$

Step 3.5.9

Multiply $- 21$ by $2$ .

$\frac{6 x - 3 - 4 x - 42}{4} = 0$

Step 3.5.10

Subtract $4 x$ from $6 x$ .

$\frac{2 x - 3 - 42}{4} = 0$

Step 3.5.11

Subtract $42$ from $- 3$ .

$\frac{2 x - 45}{4} = 0$

Step 4

Set the numerator equal to zero.

$2 x - 45 = 0$

Step 5

Solve the equation for $x$ .

Tap for more steps...

Step 5.1

Add $45$ to both sides of the equation.

$2 x = 45$

Step 5.2

Divide each term in $2 x = 45$ by $2$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $2 x = 45$ by $2$ .

$\frac{2 x}{2} = \frac{45}{2}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{45}{2}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{45}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{45}{2}$

Decimal Form:

$x = 22.5$

Mixed Number Form:

$x = 22 \frac{1}{2}$