Solve the Equation: (2x²-32)/8 = (x+4)/2 Step-by-Step

To solve the equation $\frac{2x^2-32}{8} = \frac{x+4}{2}$, let's proceed through these steps:

• Step 1: Simplify and eliminate fractions by cross-multiplying.
• Step 2: Rearrange and simplify the resulting equation.
• Step 3: Solve for the variable $x$.

Now, let's work through each step:

Step 1: Cross-multiply to eliminate the fractions.
We perform cross multiplication as follows:

$\left(2x^2 - 32\right) \times 2 = 8 \times (x + 4)$

This gives us:

$4x^2 - 64 = 8x + 32$

Step 2: Rearrange and simplify the equation.
Move all terms to one side to set the equation to zero:

$4x^2 - 8x - 96 = 0$

Simplify by dividing the entire equation by 4:

$x^2 - 2x - 24 = 0$

Step 3: Solve the quadratic equation by factoring.
Factor the quadratic equation:

$(x - 6)(x + 4) = 0$

Set each factor to zero and solve for $x$:

• $x - 6 = 0 \Rightarrow x = 6$
• $x + 4 = 0 \Rightarrow x = -4$

Considering the given multiple-choice answers, the correct solution is:

$x = 6$

Therefore, the solution to the problem is $x = 6$.