Solve for x (2x+1)/3+(4-x)/6=3

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

Step 1

Simplify $\frac{2 x + 1}{3} + \frac{4 - x}{6}$ .

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

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $1$ .

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

Subtract $x$ from $4 x$ .

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

Add $2$ and $4$ .

$\frac{3 x + 6}{6} = 3$

Factor $3$ out of $3 x + 6$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6}{6} = 3$

Factor $3$ out of $6$ .

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

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 (x + 2)}{6} = 3$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x + 2 = 2 \cdot 3$

Simplify the right side.

Multiply $2$ by $3$ .

$x + 2 = 6$

Step 4

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

Subtract $2$ from both sides of the equation.

$x = 6 - 2$

Subtract $2$ from $6$ .

$x = 4$

Solve for x (2x+1)/3+(4-x)/6=3

Related Questions

Support LCMGCF.com by disabling your adblocker.