To solve the equation [tex]\(5x + 2 = 3x + 4(2x - 1)\)[/tex] for [tex]\(x\)[/tex], we will go through the following steps:
Step 1: Distribute the 4 on the right side
First, distribute the 4 to both terms inside the parentheses:
[tex]\[
5x + 2 = 3x + 4(2x) - 4(1)
\][/tex]
Simplify the terms:
[tex]\[
5x + 2 = 3x + 8x - 4
\][/tex]
Step 2: Combine like terms on the right side
Next, combine the [tex]\(3x\)[/tex] and [tex]\(8x\)[/tex] on the right side:
[tex]\[
5x + 2 = 11x - 4
\][/tex]
Step 3: Move all terms involving [tex]\(x\)[/tex] to one side and constants to the other
To isolate [tex]\(x\)[/tex], we move all terms involving [tex]\(x\)[/tex] to one side of the equation and all constants to the other side. Start by subtracting [tex]\(11x\)[/tex] from both sides:
[tex]\[
5x - 11x + 2 = -4
\][/tex]
Simplify the equation:
[tex]\[
-6x + 2 = -4
\][/tex]
Next, move the constant term 2 to the other side by subtracting 2 from both sides:
[tex]\[
-6x + 2 - 2 = -4 - 2
\][/tex]
Simplify the equation:
[tex]\[
-6x = -6
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(-6\)[/tex]:
[tex]\[
x = \frac{-6}{-6}
\][/tex]
Simplify the result:
[tex]\[
x = 1
\][/tex]
Thus, the solution to the equation [tex]\(5x + 2 = 3x + 4(2x - 1)\)[/tex] is [tex]\(x = 1\)[/tex].
