Solve for x (x+3)/3=(10+4)/4

$\frac{x + 3}{3} = \frac{10 + 4}{4}$

Step 1

Multiply both sides of the equation by $3$ .

$3 \frac{x + 3}{3} = 3 \frac{10 + 4}{4}$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x + 3}{3} = 3 \frac{10 + 4}{4}$

Rewrite the expression.

$x + 3 = 3 \frac{10 + 4}{4}$

Simplify the right side.

Simplify $3 \frac{10 + 4}{4}$ .

Cancel the common factor of $10 + 4$ and $4$ .

Factor $2$ out of $10$ .

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

Factor $2$ out of $4$ .

$x + 3 = 3 \frac{2 \cdot 5 + 2 \cdot 2}{4}$

Factor $2$ out of $2 \cdot 5 + 2 \cdot 2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Add $5$ and $2$ .

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

Multiply $3 (\frac{7}{2})$ .

Combine $3$ and $\frac{7}{2}$ .

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

Multiply $3$ by $7$ .

$x + 3 = \frac{21}{2}$

Step 3

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

Subtract $3$ from both sides of the equation.

$x = \frac{21}{2} - 3$

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

$x = \frac{21}{2} - 3 \cdot \frac{2}{2}$

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

$x = \frac{21}{2} + \frac{- 3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$x = \frac{21 - 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$x = \frac{21 - 6}{2}$

Subtract $6$ from $21$ .

$x = \frac{15}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{2}$

Decimal Form:

$x = 7.5$

Mixed Number Form:

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

Solve for x (x+3)/3=(10+4)/4

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