Question

solve the following equation for x. express your answer in the simplest form.
\\(\frac{1}{2}(-8x + 6) - 9 = 5(3x + 5) + 8\\)
answer attempt 1 out of 2
the equation has

Explanation:

Step1: Distribute the coefficients

First, distribute $\frac{1}{2}$ on the left side and 5 on the right side:
$\frac{1}{2} \times (-8x) + \frac{1}{2} \times 6 - 9 = 5 \times 3x + 5 \times 5 + 8$
Simplify each term:
$-4x + 3 - 9 = 15x + 25 + 8$

Step2: Combine like terms

On the left side, combine $3 - 9$:
$-4x - 6 = 15x + 33$

Step3: Move variable terms to one side

Add $4x$ to both sides to get all $x$ terms on the right:
$-6 = 15x + 4x + 33$
Simplify the right side:
$-6 = 19x + 33$

Step4: Move constant terms to the other side

Subtract 33 from both sides:
$-6 - 33 = 19x$
Simplify the left side:
$-39 = 19x$

Step5: Solve for x

Divide both sides by 19:
$x = -\frac{39}{19}$

Answer:

$x = -\frac{39}{19}$ (The equation has one solution, which is $x = -\frac{39}{19}$)