Precalculus Examples

$\frac{2 x - 3}{4} + 5 = 3 x$

Step 1

Simplify $\frac{2 x - 3}{4} + 5$ .

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Step 1.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x - 3}{4} + 5 \cdot \frac{4}{4} = 3 x$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $5$ and $\frac{4}{4}$ .

$\frac{2 x - 3}{4} + \frac{5 \cdot 4}{4} = 3 x$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2 x - 3 + 5 \cdot 4}{4} = 3 x$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $5$ by $4$ .

$\frac{2 x - 3 + 20}{4} = 3 x$

Step 1.3.2

Add $- 3$ and $20$ .

$\frac{2 x + 17}{4} = 3 x$

Step 2

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

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Step 2.1

Subtract $3 x$ from both sides of the equation.

$\frac{2 x + 17}{4} - 3 x = 0$

Step 2.2

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x + 17}{4} - 3 x \cdot \frac{4}{4} = 0$

Step 2.3

Combine $- 3 x$ and $\frac{4}{4}$ .

$\frac{2 x + 17}{4} + \frac{- 3 x \cdot 4}{4} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 x + 17 - 3 x \cdot 4}{4} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $- 3$ .

$\frac{2 x + 17 - 12 x}{4} = 0$

Step 2.5.2

Subtract $12 x$ from $2 x$ .

$\frac{- 10 x + 17}{4} = 0$

Step 2.6

Factor $- 1$ out of $- 10 x$ .

$\frac{- (10 x) + 17}{4} = 0$

Step 2.7

Rewrite $17$ as $- 1 (- 17)$ .

$\frac{- (10 x) - 1 (- 17)}{4} = 0$

Step 2.8

Factor $- 1$ out of $- (10 x) - 1 (- 17)$ .

$\frac{- (10 x - 17)}{4} = 0$

Step 2.9

Rewrite $- (10 x - 17)$ as $- 1 (10 x - 17)$ .

$\frac{- 1 (10 x - 17)}{4} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{10 x - 17}{4} = 0$

Step 3

Set the numerator equal to zero.

$10 x - 17 = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Add $17$ to both sides of the equation.

$10 x = 17$

Step 4.2

Divide each term in $10 x = 17$ by $10$ and simplify.

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Step 4.2.1

Divide each term in $10 x = 17$ by $10$ .

$\frac{10 x}{10} = \frac{17}{10}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $10$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{17}{10}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{10}$

Decimal Form:

$x = 1.7$

Mixed Number Form:

$x = 1 \frac{7}{10}$