Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

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

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Step 2.5.1

Reorder $x$ and $2$ .

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

Step 2.5.2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

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

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Step 3.5.1.1.1

Factor $x$ out of $7 x$ .

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

Step 3.5.1.1.2

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

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

Step 3.5.1.1.3

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

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

Step 3.5.1.2

Multiply $2$ by $2$ .

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

Step 3.5.1.3

Add $7$ and $4$ .

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

Step 3.5.2

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

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

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $3$ by $2$ .

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

Step 4.5.2

Add $5$ and $6$ .

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

Step 5

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

$11 x = 11$

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $11$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $11$ by $11$ .

$x = 1$