Certainly! Let's solve the equation step-by-step:
Given:
[tex]\[ -5(4x - 2) = -2(3 + 6x) \][/tex]
Step 1: Distribute the constants on both sides.
On the left side, distribute [tex]\(-5\)[/tex]:
[tex]\[ -5(4x - 2) = -5 \cdot 4x + (-5) \cdot (-2) = -20x + 10 \][/tex]
On the right side, distribute [tex]\(-2\)[/tex]:
[tex]\[ -2(3 + 6x) = -2 \cdot 3 + (-2) \cdot 6x = -6 - 12x \][/tex]
So now the equation looks like this:
[tex]\[ -20x + 10 = -6 - 12x \][/tex]
Step 2: Combine like terms to isolate the variable [tex]\(x\)[/tex].
First, we want to get all the terms containing [tex]\(x\)[/tex] on one side and the constant terms on the other side.
Let's add [tex]\(12x\)[/tex] to both sides to move the [tex]\(x\)[/tex] terms together:
[tex]\[ -20x + 12x + 10 = -6 - 12x + 12x \][/tex]
[tex]\[ -8x + 10 = -6 \][/tex]
Next, subtract [tex]\(10\)[/tex] from both sides to move the constants to the other side:
[tex]\[ -8x + 10 - 10 = -6 - 10 \][/tex]
[tex]\[ -8x = -16 \][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Divide both sides of the equation by [tex]\(-8\)[/tex]:
[tex]\[ \frac{-8x}{-8} = \frac{-16}{-8} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution to the equation [tex]\( -5(4x - 2) = -2(3 + 6x) \)[/tex] is:
[tex]\[ x = 2 \][/tex]
