Precalculus Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{1}{2}$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

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

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Step 1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.3.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Multiply $2$ by $2$ .

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

Step 1.7

Add $4 x$ and $x$ .

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

Step 2

Multiply both sides by $2$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

$5 x - 3 = 1 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $1$ .

$5 x - 3 = 2$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $3$ to both sides of the equation.

$5 x = 2 + 3$

Step 4.1.2

Add $2$ and $3$ .

$5 x = 5$

Step 4.2

Divide each term in $5 x = 5$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 x = 5$ by $5$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $5$ by $5$ .

$x = 1$