Solve for x 9/4(8x-4+4/3x)=2-x

$\frac{9}{4} (8 x - 4 + \frac{4}{3} x) = 2 - x$

Step 1

Simplify $\frac{9}{4} \cdot (8 x - 4 + \frac{4}{3} x)$ .

Rewrite.

$0 + 0 + \frac{9}{4} \cdot (8 x - 4 + \frac{4}{3} x) = 2 - x$

Simplify by adding zeros.

$\frac{9}{4} \cdot (8 x - 4 + \frac{4}{3} x) = 2 - x$

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

$\frac{9}{4} \cdot (8 x - 4 + \frac{4 x}{3}) = 2 - x$

To write $8 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{4} \cdot (8 x \cdot \frac{3}{3} + \frac{4 x}{3} - 4) = 2 - x$

Simplify terms.

Combine $8 x$ and $\frac{3}{3}$ .

$\frac{9}{4} \cdot (\frac{8 x \cdot 3}{3} + \frac{4 x}{3} - 4) = 2 - x$

Combine the numerators over the common denominator.

$\frac{9}{4} \cdot (\frac{8 x \cdot 3 + 4 x}{3} - 4) = 2 - x$

Simplify the numerator.

Factor $4 x$ out of $8 x \cdot 3 + 4 x$ .

Factor $4 x$ out of $8 x \cdot 3$ .

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

Factor $4 x$ out of $4 x$ .

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

Factor $4 x$ out of $4 x (2 \cdot 3) + 4 x (1)$ .

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

Multiply $2$ by $3$ .

$\frac{9}{4} \cdot (\frac{4 x (6 + 1)}{3} - 4) = 2 - x$

Add $6$ and $1$ .

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

Multiply $7$ by $4$ .

$\frac{9}{4} \cdot (\frac{28 x}{3} - 4) = 2 - x$

Simplify terms.

Apply the distributive property.

$\frac{9}{4} \cdot \frac{28 x}{3} + \frac{9}{4} \cdot - 4 = 2 - x$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{3 (3)}{4} \cdot \frac{28 x}{3} + \frac{9}{4} \cdot - 4 = 2 - x$

Cancel the common factor.

$\frac{3 \cdot 3}{4} \cdot \frac{28 x}{3} + \frac{9}{4} \cdot - 4 = 2 - x$

Rewrite the expression.

$\frac{3}{4} (28 x) + \frac{9}{4} \cdot - 4 = 2 - x$

Cancel the common factor of $4$ .

Factor $4$ out of $28 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $7$ by $3$ .

$21 x + \frac{9}{4} \cdot - 4 = 2 - x$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$21 x + \frac{9}{4} \cdot (4 (- 1)) = 2 - x$

Cancel the common factor.

$21 x + \frac{9}{4} \cdot (4 \cdot - 1) = 2 - x$

Rewrite the expression.

$21 x + 9 \cdot - 1 = 2 - x$

Multiply $9$ by $- 1$ .

$21 x - 9 = 2 - x$

Step 2

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

Add $x$ to both sides of the equation.

$21 x - 9 + x = 2$

Add $21 x$ and $x$ .

$22 x - 9 = 2$

Step 3

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

Add $9$ to both sides of the equation.

$22 x = 2 + 9$

Add $2$ and $9$ .

$22 x = 11$

Step 4

Divide each term in $22 x = 11$ by $22$ and simplify.

Divide each term in $22 x = 11$ by $22$ .

$\frac{22 x}{22} = \frac{11}{22}$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 x}{22} = \frac{11}{22}$

Divide $x$ by $1$ .

$x = \frac{11}{22}$

Simplify the right side.

Cancel the common factor of $11$ and $22$ .

Factor $11$ out of $11$ .

$x = \frac{11 (1)}{22}$

Cancel the common factors.

Factor $11$ out of $22$ .

$x = \frac{11 \cdot 1}{11 \cdot 2}$

Cancel the common factor.

$x = \frac{11 \cdot 1}{11 \cdot 2}$

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$

Solve for x 9/4(8x-4+4/3x)=2-x

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