Solve for x 2x-7/6+x/6=(4x+3)/6

$2 x - \frac{7}{6} + \frac{x}{6} = \frac{4 x + 3}{6}$

Step 1

Multiply both sides by $6$ .

$(2 x - \frac{7}{6} + \frac{x}{6}) \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Step 2

Simplify.

Simplify the left side.

Simplify $(2 x - \frac{7}{6} + \frac{x}{6}) \cdot 6$ .

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(2 x \cdot \frac{6}{6} + \frac{x}{6} - \frac{7}{6}) \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Combine $2 x$ and $\frac{6}{6}$ .

$(\frac{2 x \cdot 6}{6} + \frac{x}{6} - \frac{7}{6}) \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Combine the numerators over the common denominator.

$(\frac{2 x \cdot 6 + x}{6} - \frac{7}{6}) \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 6 + x - 7}{6} \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Multiply $6$ by $2$ .

$\frac{12 x + x - 7}{6} \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Add $12 x$ and $x$ .

$\frac{13 x - 7}{6} \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{13 x - 7}{6} \cdot 6 = \frac{4 x + 3}{6} \cdot 6$

Rewrite the expression.

$13 x - 7 = \frac{4 x + 3}{6} \cdot 6$

Simplify the right side.

Cancel the common factor of $6$ .

Cancel the common factor.

$13 x - 7 = \frac{4 x + 3}{6} \cdot 6$

Rewrite the expression.

$13 x - 7 = 4 x + 3$

Step 3

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$13 x - 7 - 4 x = 3$

Subtract $4 x$ from $13 x$ .

$9 x - 7 = 3$

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

Add $7$ to both sides of the equation.

$9 x = 3 + 7$

Add $3$ and $7$ .

$9 x = 10$

Divide each term in $9 x = 10$ by $9$ and simplify.

Divide each term in $9 x = 10$ by $9$ .

$\frac{9 x}{9} = \frac{10}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{10}{9}$

Divide $x$ by $1$ .

$x = \frac{10}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{9}$

Decimal Form:

$x = 1.\overline{1}$

Mixed Number Form:

$x = 1 \frac{1}{9}$

Solve for x 2x-7/6+x/6=(4x+3)/6

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