Solve for x (2x-1)/4+x/3=2

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

Step 1

Simplify $\frac{2 x - 1}{4} + \frac{x}{3}$ .

To write $\frac{2 x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x - 1}{4}$ by $\frac{3}{3}$ .

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

Multiply $4$ by $3$ .

$\frac{(2 x - 1) \cdot 3}{12} + \frac{x}{3} \cdot \frac{4}{4} = 2$

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{(2 x - 1) \cdot 3}{12} + \frac{x \cdot 4}{3 \cdot 4} = 2$

Multiply $3$ by $4$ .

$\frac{(2 x - 1) \cdot 3}{12} + \frac{x \cdot 4}{12} = 2$

Combine the numerators over the common denominator.

$\frac{(2 x - 1) \cdot 3 + x \cdot 4}{12} = 2$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x \cdot 3 - 1 \cdot 3 + x \cdot 4}{12} = 2$

Multiply $3$ by $2$ .

$\frac{6 x - 1 \cdot 3 + x \cdot 4}{12} = 2$

Multiply $- 1$ by $3$ .

$\frac{6 x - 3 + x \cdot 4}{12} = 2$

Move $4$ to the left of $x$ .

$\frac{6 x - 3 + 4 \cdot x}{12} = 2$

Add $6 x$ and $4 x$ .

$\frac{10 x - 3}{12} = 2$

Step 2

Multiply both sides by $12$ .

$\frac{10 x - 3}{12} \cdot 12 = 2 \cdot 12$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{10 x - 3}{12} \cdot 12 = 2 \cdot 12$

Rewrite the expression.

$10 x - 3 = 2 \cdot 12$

Simplify the right side.

Multiply $2$ by $12$ .

$10 x - 3 = 24$

Step 4

Solve for $x$ .

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

Add $3$ to both sides of the equation.

$10 x = 24 + 3$

Add $24$ and $3$ .

$10 x = 27$

Divide each term in $10 x = 27$ by $10$ and simplify.

Divide each term in $10 x = 27$ by $10$ .

$\frac{10 x}{10} = \frac{27}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{27}{10}$

Divide $x$ by $1$ .

$x = \frac{27}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{10}$

Decimal Form:

$x = 2.7$

Mixed Number Form:

$x = 2 \frac{7}{10}$

Solve for x (2x-1)/4+x/3=2

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