Solve for x 5/2x-5/6x=4/3

$\frac{5}{2} x - \frac{5}{6} x = \frac{4}{3}$

Step 1

Simplify $\frac{5}{2} x - \frac{5}{6} x$ .

Simplify each term.

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

$\frac{5 x}{2} - \frac{5}{6} x = \frac{4}{3}$

Combine $x$ and $\frac{5}{6}$ .

$\frac{5 x}{2} - \frac{x \cdot 5}{6} = \frac{4}{3}$

Move $5$ to the left of $x$ .

$\frac{5 x}{2} - \frac{5 x}{6} = \frac{4}{3}$

To write $\frac{5 x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x}{2} \cdot \frac{3}{3} - \frac{5 x}{6} = \frac{4}{3}$

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

Multiply $\frac{5 x}{2}$ by $\frac{3}{3}$ .

$\frac{5 x \cdot 3}{2 \cdot 3} - \frac{5 x}{6} = \frac{4}{3}$

Multiply $2$ by $3$ .

$\frac{5 x \cdot 3}{6} - \frac{5 x}{6} = \frac{4}{3}$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 3 - 5 x}{6} = \frac{4}{3}$

Simplify the numerator.

Factor $5 x$ out of $5 x \cdot 3 - 5 x$ .

Factor $5 x$ out of $5 x \cdot 3$ .

$\frac{5 x (3) - 5 x}{6} = \frac{4}{3}$

Factor $5 x$ out of $- 5 x$ .

$\frac{5 x (3) + 5 x (- 1)}{6} = \frac{4}{3}$

Factor $5 x$ out of $5 x (3) + 5 x (- 1)$ .

$\frac{5 x (3 - 1)}{6} = \frac{4}{3}$

Subtract $1$ from $3$ .

$\frac{5 x \cdot 2}{6} = \frac{4}{3}$

Multiply $2$ by $5$ .

$\frac{10 x}{6} = \frac{4}{3}$

Cancel the common factor of $10$ and $6$ .

Factor $2$ out of $10 x$ .

$\frac{2 (5 x)}{6} = \frac{4}{3}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 x}{3} = \frac{4}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 x = 4$

Step 3

Divide each term in $5 x = 4$ by $5$ and simplify.

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$

Solve for x 5/2x-5/6x=4/3

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