Of course! Let's solve the equation step-by-step:
[tex]\[
\frac{2x + 3}{2} = \frac{x}{4} - 6
\][/tex]
Step 1: Eliminate the fractions
First, to eliminate the fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators. The denominators are 2 and 4, so the LCM is 4.
[tex]\[
4 \cdot \left(\frac{2x + 3}{2}\right) = 4 \cdot \left(\frac{x}{4} - 6\right)
\][/tex]
Simplify:
[tex]\[
2(2x + 3) = x - 24
\][/tex]
Step 2: Distribute and simplify
Now, distribute the 2 on the left-hand side of the equation:
[tex]\[
4x + 6 = x - 24
\][/tex]
Step 3: Isolate [tex]\(x\)[/tex]
To isolate [tex]\(x\)[/tex], first subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[
4x + 6 - x = -24
\][/tex]
This simplifies to:
[tex]\[
3x + 6 = -24
\][/tex]
Next, subtract 6 from both sides of the equation:
[tex]\[
3x + 6 - 6 = -24 - 6
\][/tex]
Which simplifies to:
[tex]\[
3x = -30
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex]
Finally, divide both sides by 3:
[tex]\[
x = \frac{-30}{3}
\][/tex]
[tex]\[
x = -10
\][/tex]
So, the solution to the equation is:
[tex]\[
\boxed{-10}
\][/tex]
