Question

solve for w.
33 = (6w + 9)/2 + (w - 3)/4
simplify your answer as much as possible.
w = \boxed{}

Explanation:

Step1: Eliminate denominators

Multiply all terms by 4:
$$4\times33 = 4\times\frac{6w+9}{2} + 4\times\frac{w-3}{4}$$
$$132 = 2(6w+9) + (w-3)$$

Step2: Expand parentheses

Distribute the coefficients:
$$132 = 12w + 18 + w - 3$$

Step3: Combine like terms

Combine variable and constant terms:
$$132 = 13w + 15$$

Step4: Isolate constant terms

Subtract 15 from both sides:
$$132 - 15 = 13w$$
$$117 = 13w$$

Step5: Solve for w

Divide both sides by 13:
$$w = \frac{117}{13}$$
$$w = 9$$

Answer:

$w = 9$