Certainly! Let's solve the equation step by step:
Given:
[tex]\[
\frac{3(2x + 1)}{5} = 2x - 5
\][/tex]
### Step 1: Eliminate the Fraction
To eliminate the fraction, we'll multiply both sides of the equation by [tex]\(5\)[/tex]:
[tex]\[
5 \times \frac{3(2x + 1)}{5} = 5 \times (2x - 5)
\][/tex]
This simplifies to:
[tex]\[
3(2x + 1) = 5(2x - 5)
\][/tex]
### Step 2: Distribute the Constants
Distribute [tex]\(3\)[/tex] on the left-hand side:
[tex]\[
3 \times 2x + 3 \times 1 = 6x + 3
\][/tex]
Distribute [tex]\(5\)[/tex] on the right-hand side:
[tex]\[
5 \times 2x - 5 \times 5 = 10x - 25
\][/tex]
Now rewrite the equation:
[tex]\[
6x + 3 = 10x - 25
\][/tex]
### Step 3: Collect Like Terms
Move all the terms involving [tex]\(x\)[/tex] to one side of the equation and the constant terms to the other side. Subtract [tex]\(10x\)[/tex] from both sides:
[tex]\[
6x + 3 - 10x = 10x - 25 - 10x
\][/tex]
This simplifies to:
[tex]\[
-4x + 3 = -25
\][/tex]
Now, subtract [tex]\(3\)[/tex] from both sides to collect the constant terms on the right:
[tex]\[
-4x + 3 - 3 = -25 - 3
\][/tex]
This simplifies to:
[tex]\[
-4x = -28
\][/tex]
### Step 4: Solve for [tex]\(x\)[/tex]
Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-28}{-4}
\][/tex]
This simplifies to:
[tex]\[
x = 7
\][/tex]
So, the solution to the equation is:
[tex]\[
x = 7.0
\][/tex]
