Question

solve for w.
\\(\frac{6w + 5}{5} - \frac{8w + 2}{3} = -7\\)
simplify your answer as much as possible.
\\(w = \\)

Explanation:

Step1: Eliminate denominators

Multiply all terms by 15 (LCM of 5 and 3):
$$15 \times \frac{6w+5}{5} - 15 \times \frac{8w+2}{3} = 15 \times (-7)$$
Simplify each term:
$$3(6w+5) - 5(8w+2) = -105$$

Step2: Expand parentheses

Distribute the coefficients:
$$18w + 15 - 40w - 10 = -105$$

Step3: Combine like terms

Combine variable and constant terms:
$$(18w-40w) + (15-10) = -105$$
$$-22w + 5 = -105$$

Step4: Isolate variable term

Subtract 5 from both sides:
$$-22w = -105 - 5$$
$$-22w = -110$$

Step5: Solve for w

Divide both sides by -22:
$$w = \frac{-110}{-22}$$

Answer:

$w = 5$