Solve for x 1/2(7x-6)=6x-10

$\frac{1}{2} (7 x - 6) = 6 x - 10$

Simplify $\frac{1}{2} \cdot (7 x - 6)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (7 x - 6) = 6 x - 10$

Simplify by adding zeros.

$\frac{1}{2} \cdot (7 x - 6) = 6 x - 10$

Apply the distributive property.

$\frac{1}{2} (7 x) + \frac{1}{2} \cdot - 6 = 6 x - 10$

Multiply $\frac{1}{2} (7 x)$ .

Combine $7$ and $\frac{1}{2}$ .

$\frac{7}{2} x + \frac{1}{2} \cdot - 6 = 6 x - 10$

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

$\frac{7 x}{2} + \frac{1}{2} \cdot - 6 = 6 x - 10$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$\frac{7 x}{2} + \frac{1}{2} \cdot (2 (- 3)) = 6 x - 10$

Cancel the common factor.

$\frac{7 x}{2} + \frac{1}{2} \cdot (2 \cdot - 3) = 6 x - 10$

Rewrite the expression.

$\frac{7 x}{2} - 3 = 6 x - 10$

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

Subtract $6 x$ from both sides of the equation.

$\frac{7 x}{2} - 3 - 6 x = - 10$

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

$\frac{7 x}{2} - 6 x \cdot \frac{2}{2} - 3 = - 10$

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

$\frac{7 x}{2} + \frac{- 6 x \cdot 2}{2} - 3 = - 10$

Combine the numerators over the common denominator.

$\frac{7 x - 6 x \cdot 2}{2} - 3 = - 10$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x - 6 x \cdot 2$ .

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - 6 x \cdot 2}{2} - 3 = - 10$

Factor $x$ out of $- 6 x \cdot 2$ .

$\frac{x \cdot 7 + x (- 6 \cdot 2)}{2} - 3 = - 10$

Factor $x$ out of $x \cdot 7 + x (- 6 \cdot 2)$ .

$\frac{x (7 - 6 \cdot 2)}{2} - 3 = - 10$

Multiply $- 6$ by $2$ .

$\frac{x (7 - 12)}{2} - 3 = - 10$

Subtract $12$ from $7$ .

$\frac{x \cdot - 5}{2} - 3 = - 10$

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

$\frac{- 5 \cdot x}{2} - 3 = - 10$

Move the negative in front of the fraction.

$- \frac{5 x}{2} - 3 = - 10$

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

Add $3$ to both sides of the equation.

$- \frac{5 x}{2} = - 10 + 3$

Add $- 10$ and $3$ .

$- \frac{5 x}{2} = - 7$

Multiply both sides of the equation by $- \frac{2}{5}$ .

$- \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{5} (- \frac{5 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot - 7$

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$\frac{- 2}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 7$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 7$

Cancel the common factor.

$\frac{2 \cdot - 1}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 7$

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{2}{5} \cdot - 7$

Cancel the common factor of $5$ .

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

$\frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot - 7$

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot - 7$

Rewrite the expression.

$- - x = - \frac{2}{5} \cdot - 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{5} \cdot - 7$

Multiply $x$ by $1$ .

$x = - \frac{2}{5} \cdot - 7$

Simplify the right side.

Multiply $- \frac{2}{5} \cdot - 7$ .

Multiply $- 7$ by $- 1$ .

$x = 7 (\frac{2}{5})$

Combine $7$ and $\frac{2}{5}$ .

$x = \frac{7 \cdot 2}{5}$

Multiply $7$ by $2$ .

$x = \frac{14}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{14}{5}$

Decimal Form:

$x = 2.8$

Mixed Number Form:

$x = 2 \frac{4}{5}$

Solve for x 1/2(7x-6)=6x-10

Related Questions

Support LCMGCF.com by disabling your adblocker.