Solve for x -1/2x-1/4(10x-9)=-(-7/4x+2)-x

$- \frac{1}{2} x - \frac{1}{4} (10 x - 9) = - (- \frac{7}{4} x + 2) - x$

Step 1

Simplify $- \frac{1}{2} x - \frac{1}{4} \cdot (10 x - 9)$ .

Simplify each term.

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

$- \frac{x}{2} - \frac{1}{4} \cdot (10 x - 9) = - (- \frac{7}{4} x + 2) - x$

Apply the distributive property.

$- \frac{x}{2} - \frac{1}{4} (10 x) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- \frac{x}{2} + \frac{- 1}{4} (10 x) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Factor $2$ out of $4$ .

$- \frac{x}{2} + \frac{- 1}{2 (2)} (10 x) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Factor $2$ out of $10 x$ .

$- \frac{x}{2} + \frac{- 1}{2 (2)} (2 (5 x)) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Cancel the common factor.

$- \frac{x}{2} + \frac{- 1}{2 \cdot 2} (2 (5 x)) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Rewrite the expression.

$- \frac{x}{2} + \frac{- 1}{2} (5 x) - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Combine $5$ and $\frac{- 1}{2}$ .

$- \frac{x}{2} + \frac{5 \cdot - 1}{2} x - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Multiply $5$ by $- 1$ .

$- \frac{x}{2} + \frac{- 5}{2} x - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

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

$- \frac{x}{2} + \frac{- 5 x}{2} - \frac{1}{4} \cdot - 9 = - (- \frac{7}{4} x + 2) - x$

Multiply $- \frac{1}{4} \cdot - 9$ .

Multiply $- 9$ by $- 1$ .

$- \frac{x}{2} + \frac{- 5 x}{2} + 9 (\frac{1}{4}) = - (- \frac{7}{4} x + 2) - x$

Combine $9$ and $\frac{1}{4}$ .

$- \frac{x}{2} + \frac{- 5 x}{2} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{5 x}{2} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{- x - 5 x}{2} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Subtract $5 x$ from $- x$ .

$\frac{- 6 x}{2} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Cancel the common factor of $- 6$ and $2$ .

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

$\frac{2 (- 3 x)}{2} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (- 3 x)}{2 (1)} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Cancel the common factor.

$\frac{2 (- 3 x)}{2 \cdot 1} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Rewrite the expression.

$\frac{- 3 x}{1} + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Divide $- 3 x$ by $1$ .

$- 3 x + \frac{9}{4} = - (- \frac{7}{4} x + 2) - x$

Step 2

Simplify $- (- \frac{7}{4} x + 2) - x$ .

Simplify each term.

Combine $x$ and $\frac{7}{4}$ .

$- 3 x + \frac{9}{4} = - (- \frac{x \cdot 7}{4} + 2) - x$

Move $7$ to the left of $x$ .

$- 3 x + \frac{9}{4} = - (- \frac{7 x}{4} + 2) - x$

Apply the distributive property.

$- 3 x + \frac{9}{4} = - - \frac{7 x}{4} - 1 \cdot 2 - x$

Multiply $- - \frac{7 x}{4}$ .

Multiply $- 1$ by $- 1$ .

$- 3 x + \frac{9}{4} = 1 \frac{7 x}{4} - 1 \cdot 2 - x$

Multiply $\frac{7 x}{4}$ by $1$ .

$- 3 x + \frac{9}{4} = \frac{7 x}{4} - 1 \cdot 2 - x$

Multiply $- 1$ by $2$ .

$- 3 x + \frac{9}{4} = \frac{7 x}{4} - 2 - x$

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

$- 3 x + \frac{9}{4} = \frac{7 x}{4} - x \cdot \frac{4}{4} - 2$

Simplify terms.

Combine $- x$ and $\frac{4}{4}$ .

$- 3 x + \frac{9}{4} = \frac{7 x}{4} + \frac{- x \cdot 4}{4} - 2$

Combine the numerators over the common denominator.

$- 3 x + \frac{9}{4} = \frac{7 x - x \cdot 4}{4} - 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x - x \cdot 4$ .

Factor $x$ out of $7 x$ .

$- 3 x + \frac{9}{4} = \frac{x \cdot 7 - x \cdot 4}{4} - 2$

Factor $x$ out of $- x \cdot 4$ .

$- 3 x + \frac{9}{4} = \frac{x \cdot 7 + x (- 1 \cdot 4)}{4} - 2$

Factor $x$ out of $x \cdot 7 + x (- 1 \cdot 4)$ .

$- 3 x + \frac{9}{4} = \frac{x (7 - 1 \cdot 4)}{4} - 2$

Multiply $- 1$ by $4$ .

$- 3 x + \frac{9}{4} = \frac{x (7 - 4)}{4} - 2$

Subtract $4$ from $7$ .

$- 3 x + \frac{9}{4} = \frac{x \cdot 3}{4} - 2$

Move $3$ to the left of $x$ .

$- 3 x + \frac{9}{4} = \frac{3 x}{4} - 2$

Step 3

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

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$- 3 x + \frac{9}{4} - \frac{3 x}{4} = - 2$

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

$- 3 x \cdot \frac{4}{4} - \frac{3 x}{4} + \frac{9}{4} = - 2$

Combine $- 3 x$ and $\frac{4}{4}$ .

$\frac{- 3 x \cdot 4}{4} - \frac{3 x}{4} + \frac{9}{4} = - 2$

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 4 - 3 x}{4} + \frac{9}{4} = - 2$

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 4 - 3 x + 9}{4} = - 2$

Multiply $4$ by $- 3$ .

$\frac{- 12 x - 3 x + 9}{4} = - 2$

Subtract $3 x$ from $- 12 x$ .

$\frac{- 15 x + 9}{4} = - 2$

Factor $3$ out of $- 15 x + 9$ .

Factor $3$ out of $- 15 x$ .

$\frac{3 (- 5 x) + 9}{4} = - 2$

Factor $3$ out of $9$ .

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

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

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

Factor $- 1$ out of $- 5 x$ .

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

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{3 (- (5 x) - 1 (- 3))}{4} = - 2$

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

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

Rewrite $- (5 x - 3)$ as $- 1 (5 x - 3)$ .

$\frac{3 (- 1 (5 x - 3))}{4} = - 2$

Move the negative in front of the fraction.

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

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 (5 x - 3)}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 (5 x - 3)}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 (5 x - 3)}{4} = - \frac{4}{3} \cdot - 2$

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 (5 x - 3)}{4} = - \frac{4}{3} \cdot - 2$

Rewrite the expression.

$\frac{- 1}{3} (- 3 (5 x - 3)) = - \frac{4}{3} \cdot - 2$

Cancel the common factor of $3$ .

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

$\frac{- 1}{3} (3 (- (5 x - 3))) = - \frac{4}{3} \cdot - 2$

Cancel the common factor.

$\frac{- 1}{3} (3 (- (5 x - 3))) = - \frac{4}{3} \cdot - 2$

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (5 x - 3) = - \frac{4}{3} \cdot - 2$

Multiply $5 x - 3$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{4}{3} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

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

Combine $2$ and $\frac{4}{3}$ .

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

Multiply $2$ by $4$ .

$5 x - 3 = \frac{8}{3}$

Step 6

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

Add $3$ to both sides of the equation.

$5 x = \frac{8}{3} + 3$

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

$5 x = \frac{8}{3} + 3 \cdot \frac{3}{3}$

Combine $3$ and $\frac{3}{3}$ .

$5 x = \frac{8}{3} + \frac{3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$5 x = \frac{8 + 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$5 x = \frac{8 + 9}{3}$

Add $8$ and $9$ .

$5 x = \frac{17}{3}$

Step 7

Divide each term in $5 x = \frac{17}{3}$ by $5$ and simplify.

Divide each term in $5 x = \frac{17}{3}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{17}{3}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{17}{3}}{5}$

Divide $x$ by $1$ .

$x = \frac{\frac{17}{3}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{17}{3} \cdot \frac{1}{5}$

Multiply $\frac{17}{3} \cdot \frac{1}{5}$ .

Multiply $\frac{17}{3}$ by $\frac{1}{5}$ .

$x = \frac{17}{3 \cdot 5}$

Multiply $3$ by $5$ .

$x = \frac{17}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{15}$

Decimal Form:

$x = 1.1\overline{3}$

Mixed Number Form:

$x = 1 \frac{2}{15}$

Solve for x -1/2x-1/4(10x-9)=-(-7/4x+2)-x

Related Questions

Support LCMGCF.com by disabling your adblocker.