Solve for x 5/2-2x=5/2x-3+x

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $5 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Add $5 x$ and $2 \cdot x$ .

$\frac{7 x}{2} - 3 = \frac{5}{2} - 2 x$

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$\frac{7 x}{2} - 3 + 2 x = \frac{5}{2}$

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

$\frac{7 x}{2} + 2 x \cdot \frac{2}{2} - 3 = \frac{5}{2}$

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

$\frac{7 x}{2} + \frac{2 x \cdot 2}{2} - 3 = \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{7 x + 2 x \cdot 2}{2} - 3 = \frac{5}{2}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x + 2 x \cdot 2$ .

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 + 2 x \cdot 2}{2} - 3 = \frac{5}{2}$

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

$\frac{x \cdot 7 + x (2 \cdot 2)}{2} - 3 = \frac{5}{2}$

Factor $x$ out of $x \cdot 7 + x (2 \cdot 2)$ .

$\frac{x (7 + 2 \cdot 2)}{2} - 3 = \frac{5}{2}$

Multiply $2$ by $2$ .

$\frac{x (7 + 4)}{2} - 3 = \frac{5}{2}$

Add $7$ and $4$ .

$\frac{x \cdot 11}{2} - 3 = \frac{5}{2}$

Move $11$ to the left of $x$ .

$\frac{11 x}{2} - 3 = \frac{5}{2}$

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

Add $3$ to both sides of the equation.

$\frac{11 x}{2} = \frac{5}{2} + 3$

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

$\frac{11 x}{2} = \frac{5}{2} + 3 \cdot \frac{2}{2}$

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

$\frac{11 x}{2} = \frac{5}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{11 x}{2} = \frac{5 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{11 x}{2} = \frac{5 + 6}{2}$

Add $5$ and $6$ .

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

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

$11 x = 11$

Divide each term in $11 x = 11$ by $11$ and simplify.

Divide each term in $11 x = 11$ by $11$ .

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

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $11$ by $11$ .

$x = 1$

Solve for x 5/2-2x=5/2x-3+x

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