Pre-Algebra Examples

$\frac{2 x - 1}{25} + \frac{3 x}{5} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1

Simplify $\frac{2 x - 1}{25} + \frac{3 x}{5} + 2$ .

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Step 1.1

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x - 1}{25} + \frac{3 x}{5} \cdot \frac{5}{5} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.2

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{3 x}{5}$ by $\frac{5}{5}$ .

$\frac{2 x - 1}{25} + \frac{3 x \cdot 5}{5 \cdot 5} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.2.2

Multiply $5$ by $5$ .

$\frac{2 x - 1}{25} + \frac{3 x \cdot 5}{25} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{2 x - 1 + 3 x \cdot 5}{25} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $5$ by $3$ .

$\frac{2 x - 1 + 15 x}{25} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.4.2

Add $2 x$ and $15 x$ .

$\frac{17 x - 1}{25} + 2 = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.5

To write $2$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{17 x - 1}{25} + 2 \cdot \frac{25}{25} = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.6

Simplify terms.

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Step 1.6.1

Combine $2$ and $\frac{25}{25}$ .

$\frac{17 x - 1}{25} + \frac{2 \cdot 25}{25} = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.6.2

Combine the numerators over the common denominator.

$\frac{17 x - 1 + 2 \cdot 25}{25} = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $2$ by $25$ .

$\frac{17 x - 1 + 50}{25} = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 1.7.2

Add $- 1$ and $50$ .

$\frac{17 x + 49}{25} = \frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 2

Simplify $\frac{4 x}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $4$ and $10$ .

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Step 2.1.1.1

Factor $2$ out of $4 x$ .

$\frac{17 x + 49}{25} = \frac{2 (2 x)}{10} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 2.1.1.2

Cancel the common factors.

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Step 2.1.1.2.1

Factor $2$ out of $10$ .

$\frac{17 x + 49}{25} = \frac{2 (2 x)}{2 (5)} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{17 x + 49}{25} = \frac{2 (2 x)}{2 \cdot 5} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{17 x + 49}{25} = \frac{2 x}{5} - \frac{3 x (- 1)}{5} - \frac{3}{2}$

Step 2.1.2

Multiply $- 1$ by $3$ .

$\frac{17 x + 49}{25} = \frac{2 x}{5} - \frac{- 3 x}{5} - \frac{3}{2}$

Step 2.1.3

Move the negative in front of the fraction.

$\frac{17 x + 49}{25} = \frac{2 x}{5} - - \frac{3 x}{5} - \frac{3}{2}$

Step 2.1.4

Multiply $- - \frac{3 x}{5}$ .

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Step 2.1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{17 x + 49}{25} = \frac{2 x}{5} + 1 \frac{3 x}{5} - \frac{3}{2}$

Step 2.1.4.2

Multiply $\frac{3 x}{5}$ by $1$ .

$\frac{17 x + 49}{25} = \frac{2 x}{5} + \frac{3 x}{5} - \frac{3}{2}$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$\frac{17 x + 49}{25} = \frac{2 x + 3 x}{5} + \frac{- 3}{2}$

Step 2.2.2

Add $2 x$ and $3 x$ .

$\frac{17 x + 49}{25} = \frac{5 x}{5} + \frac{- 3}{2}$

Step 2.3

Simplify each term.

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Step 2.3.1

Cancel the common factor of $5$ .

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Step 2.3.1.1

Cancel the common factor.

$\frac{17 x + 49}{25} = \frac{5 x}{5} + \frac{- 3}{2}$

Step 2.3.1.2

Divide $x$ by $1$ .

$\frac{17 x + 49}{25} = x + \frac{- 3}{2}$

Step 2.3.2

Move the negative in front of the fraction.

$\frac{17 x + 49}{25} = x - \frac{3}{2}$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 10.8125$

Step 4