Solve for x 4x-x/2-3=1/2

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

Step 1

Simplify $4 x - \frac{x}{2} - 3$ .

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Simplify terms.

Combine $4 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x \cdot 2 - x$ .

Factor $x$ out of $4 x \cdot 2$ .

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 1$ .

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

Multiply $4$ by $2$ .

$\frac{x (8 - 1)}{2} - 3 = \frac{1}{2}$

Subtract $1$ from $8$ .

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

Move $7$ to the left of $x$ .

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

Step 2

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

Add $3$ to both sides of the equation.

$\frac{7 x}{2} = \frac{1}{2} + 3$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{7 x}{2} = \frac{1 + 6}{2}$

Add $1$ and $6$ .

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 x = 7$

Step 4

Divide each term in $7 x = 7$ by $7$ and simplify.

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$x = 1$

Solve for x 4x-x/2-3=1/2

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