Sure! Let's solve the given equation step by step and prove [tex]\( y = 3 \)[/tex].
Given equation:
[tex]\[ \frac{5y - 1}{2} = 7 \][/tex]
Step-by-Step Solution:
1. Multiply both sides by 2:
[tex]\[
\frac{5y - 1}{2} \times 2 = 7 \times 2
\][/tex]
This gives:
[tex]\[
5y - 1 = 14
\][/tex]
Reason: To eliminate the fraction.
2. Add 1 to both sides:
[tex]\[
5y - 1 + 1 = 14 + 1
\][/tex]
This simplifies to:
[tex]\[
5y = 15
\][/tex]
Reason: To isolate the term with the variable [tex]\( y \)[/tex].
3. Divide both sides by 5:
[tex]\[
\frac{5y}{5} = \frac{15}{5}
\][/tex]
This simplifies to:
[tex]\[
y = 3
\][/tex]
Reason: To solve for [tex]\( y \)[/tex].
Thus, we have proved that:
[tex]\[ y = 3 \][/tex]
To summarize:
[tex]\[
\frac{5y - 1}{2} = 7 \quad \text{(Given)}
\][/tex]
[tex]\[
\implies 5y - 1 = 14 \quad \text{(Multiplying both sides by 2)}
\][/tex]
[tex]\[
\implies 5y = 15 \quad \text{(Adding 1 to both sides)}
\][/tex]
[tex]\[
\implies y = 3 \quad \text{(Dividing both sides by 5)}
\][/tex]
Hence, we have proved that [tex]\( y = 3 \)[/tex].
