Trigonometry Examples

$7 - \frac{3 x - 1}{2} = - \frac{3}{4}$

Step 1

Simplify $7 - \frac{3 x - 1}{2}$ .

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Step 1.1

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

$7 \cdot \frac{2}{2} - \frac{3 x - 1}{2} = - \frac{3}{4}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $7$ and $\frac{2}{2}$ .

$\frac{7 \cdot 2}{2} - \frac{3 x - 1}{2} = - \frac{3}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 - (3 x - 1)}{2} = - \frac{3}{4}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $7$ by $2$ .

$\frac{14 - (3 x - 1)}{2} = - \frac{3}{4}$

Step 1.3.2

Apply the distributive property.

$\frac{14 - (3 x) - - 1}{2} = - \frac{3}{4}$

Step 1.3.3

Multiply $3$ by $- 1$ .

$\frac{14 - 3 x - - 1}{2} = - \frac{3}{4}$

Step 1.3.4

Multiply $- 1$ by $- 1$ .

$\frac{14 - 3 x + 1}{2} = - \frac{3}{4}$

Step 1.3.5

Add $14$ and $1$ .

$\frac{- 3 x + 15}{2} = - \frac{3}{4}$

Step 1.3.6

Factor $3$ out of $- 3 x + 15$ .

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Step 1.3.6.1

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

$\frac{3 (- x) + 15}{2} = - \frac{3}{4}$

Step 1.3.6.2

Factor $3$ out of $15$ .

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

Step 1.3.6.3

Factor $3$ out of $3 (- x) + 3 (5)$ .

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

Step 1.4

Simplify with factoring out.

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Step 1.4.1

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

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

Step 1.4.2

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 1.4.3

Factor $- 1$ out of $- (x) - 1 (- 5)$ .

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

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (x - 5)$ as $- 1 (x - 5)$ .

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

Step 1.4.4.2

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 3.1.1.1.2

Move the leading negative in $- \frac{3 (x - 5)}{2}$ into the numerator.

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

Step 3.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 3.1.1.1.4

Cancel the common factor.

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

Step 3.1.1.1.5

Rewrite the expression.

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

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $- 3 (x - 5)$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.3.2

Multiply $x - 5$ by $1$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{2}{3} (- \frac{3}{4})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 3.2.1.1.2

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Step 3.2.1.1.3

Factor $2$ out of $- 2$ .

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

Step 3.2.1.1.4

Factor $2$ out of $4$ .

$x - 5 = \frac{2 \cdot - 1}{3} \cdot \frac{- 3}{2 \cdot 2}$

Step 3.2.1.1.5

Cancel the common factor.

$x - 5 = \frac{2 \cdot - 1}{3} \cdot \frac{- 3}{2 \cdot 2}$

Step 3.2.1.1.6

Rewrite the expression.

$x - 5 = \frac{- 1}{3} \cdot \frac{- 3}{2}$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Factor $3$ out of $- 3$ .

$x - 5 = \frac{- 1}{3} \cdot \frac{3 (- 1)}{2}$

Step 3.2.1.2.2

Cancel the common factor.

$x - 5 = \frac{- 1}{3} \cdot \frac{3 \cdot - 1}{2}$

Step 3.2.1.2.3

Rewrite the expression.

$x - 5 = - \frac{- 1}{2}$

Step 3.2.1.3

Move the negative in front of the fraction.

$x - 5 = - - \frac{1}{2}$

Step 3.2.1.4

Multiply $- - \frac{1}{2}$ .

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Step 3.2.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2.1.4.2

Multiply $\frac{1}{2}$ by $1$ .

$x - 5 = \frac{1}{2}$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$x = \frac{1}{2} + 5$

Step 4.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{1}{2} + 5 \cdot \frac{2}{2}$

Step 4.3

Combine $5$ and $\frac{2}{2}$ .

$x = \frac{1}{2} + \frac{5 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{1 + 5 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $5$ by $2$ .

$x = \frac{1 + 10}{2}$

Step 4.5.2

Add $1$ and $10$ .

$x = \frac{11}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}$

Decimal Form:

$x = 5.5$

Mixed Number Form:

$x = 5 \frac{1}{2}$