Algebra Examples

$\frac{5}{2} x + \frac{x - 4}{2} = 11$

Step 1

Simplify $\frac{5}{2} x + \frac{x - 4}{2}$ .

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Step 1.1

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

$\frac{5 x}{2} + \frac{x - 4}{2} = 11$

Step 1.2

Combine the numerators over the common denominator.

$\frac{5 x + x - 4}{2} = 11$

Step 1.3

Add $5 x$ and $x$ .

$\frac{6 x - 4}{2} = 11$

Step 1.4

Cancel the common factor of $6 x - 4$ and $2$ .

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Step 1.4.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x) - 4}{2} = 11$

Step 1.4.2

Factor $2$ out of $- 4$ .

$\frac{2 (3 x) + 2 \cdot - 2}{2} = 11$

Step 1.4.3

Factor $2$ out of $2 (3 x) + 2 (- 2)$ .

$\frac{2 (3 x - 2)}{2} = 11$

Step 1.4.4

Cancel the common factors.

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Step 1.4.4.1

Factor $2$ out of $2$ .

$\frac{2 (3 x - 2)}{2 (1)} = 11$

Step 1.4.4.2

Cancel the common factor.

$\frac{2 (3 x - 2)}{2 \cdot 1} = 11$

Step 1.4.4.3

Rewrite the expression.

$\frac{3 x - 2}{1} = 11$

Step 1.4.4.4

Divide $3 x - 2$ by $1$ .

$3 x - 2 = 11$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

$3 x = 11 + 2$

Step 2.2

Add $11$ and $2$ .

$3 x = 13$

Step 3

Divide each term in $3 x = 13$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = 13$ by $3$ .

$\frac{3 x}{3} = \frac{13}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{13}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{13}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{3}$

Decimal Form:

$x = 4.\overline{3}$

Mixed Number Form:

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