Solve for x 2x+1 1/2=3 1/2

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

Step 1

Simplify the left side.

Convert $1 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $1$ and $\frac{1}{2}$ .

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

Step 2

Simplify the right side.

Convert $3 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $3$ and $\frac{1}{2}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$2 x + \frac{3}{2} = \frac{6 + 1}{2}$

Add $6$ and $1$ .

$2 x + \frac{3}{2} = \frac{7}{2}$

Step 3

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

Subtract $\frac{3}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $7$ .

$2 x = \frac{4}{2}$

Divide $4$ by $2$ .

$2 x = 2$

Step 4

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

Solve for x 2x+1 1/2=3 1/2

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