Question

solve for x.
$\frac{9}{4}left(8x - 4 + \frac{4}{3}x
ight) = 2 - x$
$x = square$

Explanation:

Step1: Simplify inside the parentheses

Combine like terms inside the parentheses:
$$8x + \frac{4}{3}x - 4 = \frac{24x + 4x}{3} - 4 = \frac{28x}{3} - 4$$

Step2: Distribute the $\frac{9}{4}$ factor

Multiply each term inside by $\frac{9}{4}$:
$$\frac{9}{4} \times \frac{28x}{3} - \frac{9}{4} \times 4 = 2 - x$$
$$21x - 9 = 2 - x$$

Step3: Isolate x terms on one side

Add $x$ to both sides:
$$21x + x - 9 = 2$$
$$22x - 9 = 2$$

Step4: Isolate the x term

Add 9 to both sides:
$$22x = 2 + 9$$
$$22x = 11$$

Step5: Solve for x

Divide both sides by 22:
$$x = \frac{11}{22} = \frac{1}{2}$$

Answer:

$\frac{1}{2}$