Certainly! Let's solve the given equation step-by-step. We're given the equation:
[tex]\[
\frac{4X + 5}{6} = \frac{7}{2}
\][/tex]
### Step 1: Eliminate the fraction by multiplying both sides by 6.
To remove the fraction, multiply both sides of the equation by 6:
[tex]\[
6 \cdot \frac{4X + 5}{6} = 6 \cdot \frac{7}{2}
\][/tex]
This simplifies to:
[tex]\[
4X + 5 = \frac{7 \cdot 6}{2}
\][/tex]
### Step 2: Simplify the right-hand side.
Calculate the value on the right-hand side:
[tex]\[
\frac{7 \cdot 6}{2} = \frac{42}{2} = 21
\][/tex]
So now our equation is simplified to:
[tex]\[
4X + 5 = 21
\][/tex]
### Step 3: Isolate the variable term.
Next, isolate [tex]\(4X\)[/tex] by subtracting 5 from both sides of the equation:
[tex]\[
4X + 5 - 5 = 21 - 5
\][/tex]
Which simplifies to:
[tex]\[
4X = 16
\][/tex]
### Step 4: Solve for [tex]\(X\)[/tex].
Finally, solve for [tex]\(X\)[/tex] by dividing both sides by 4:
[tex]\[
\frac{4X}{4} = \frac{16}{4}
\][/tex]
This gives us:
[tex]\[
X = 4
\][/tex]
### Final Answer
The solution to the equation [tex]\(\frac{4X + 5}{6} = \frac{7}{2}\)[/tex] is:
[tex]\[
X = 4
\][/tex]
