Precalculus Examples

$x - \frac{4 (- 25)}{14} - \frac{7}{2} = 5$

Step 1

Simplify $x - \frac{4 (- 25)}{14} - \frac{7}{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $4$ and $14$ .

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Step 1.1.1.1

Factor $2$ out of $4 (- 25)$ .

$x - \frac{2 (2 \cdot - 25)}{14} - \frac{7}{2} = 5$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $14$ .

$x - \frac{2 (2 \cdot - 25)}{2 (7)} - \frac{7}{2} = 5$

Step 1.1.1.2.2

Cancel the common factor.

$x - \frac{2 (2 \cdot - 25)}{2 \cdot 7} - \frac{7}{2} = 5$

Step 1.1.1.2.3

Rewrite the expression.

$x - \frac{2 \cdot - 25}{7} - \frac{7}{2} = 5$

Step 1.1.2

Multiply $2$ by $- 25$ .

$x - \frac{- 50}{7} - \frac{7}{2} = 5$

Step 1.1.3

Move the negative in front of the fraction.

$x - - \frac{50}{7} - \frac{7}{2} = 5$

Step 1.1.4

Multiply $- - \frac{50}{7}$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

$x + 1 (\frac{50}{7}) - \frac{7}{2} = 5$

Step 1.1.4.2

Multiply $\frac{50}{7}$ by $1$ .

$x + \frac{50}{7} - \frac{7}{2} = 5$

Step 1.2

To write $\frac{50}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + \frac{50}{7} \cdot \frac{2}{2} - \frac{7}{2} = 5$

Step 1.3

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x + \frac{50}{7} \cdot \frac{2}{2} - \frac{7}{2} \cdot \frac{7}{7} = 5$

Step 1.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{50}{7}$ by $\frac{2}{2}$ .

$x + \frac{50 \cdot 2}{7 \cdot 2} - \frac{7}{2} \cdot \frac{7}{7} = 5$

Step 1.4.2

Multiply $7$ by $2$ .

$x + \frac{50 \cdot 2}{14} - \frac{7}{2} \cdot \frac{7}{7} = 5$

Step 1.4.3

Multiply $\frac{7}{2}$ by $\frac{7}{7}$ .

$x + \frac{50 \cdot 2}{14} - \frac{7 \cdot 7}{2 \cdot 7} = 5$

Step 1.4.4

Multiply $2$ by $7$ .

$x + \frac{50 \cdot 2}{14} - \frac{7 \cdot 7}{14} = 5$

Step 1.5

Combine the numerators over the common denominator.

$x + \frac{50 \cdot 2 - 7 \cdot 7}{14} = 5$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $50$ by $2$ .

$x + \frac{100 - 7 \cdot 7}{14} = 5$

Step 1.6.2

Multiply $- 7$ by $7$ .

$x + \frac{100 - 49}{14} = 5$

Step 1.6.3

Subtract $49$ from $100$ .

$x + \frac{51}{14} = 5$

Step 2

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

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Step 2.1

Subtract $\frac{51}{14}$ from both sides of the equation.

$x = 5 - \frac{51}{14}$

Step 2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$x = 5 \cdot \frac{14}{14} - \frac{51}{14}$

Step 2.3

Combine $5$ and $\frac{14}{14}$ .

$x = \frac{5 \cdot 14}{14} - \frac{51}{14}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{5 \cdot 14 - 51}{14}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $14$ .

$x = \frac{70 - 51}{14}$

Step 2.5.2

Subtract $51$ from $70$ .

$x = \frac{19}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{14}$

Decimal Form:

$x = 1.35714285 \dots$

Mixed Number Form:

$x = 1 \frac{5}{14}$