Sure, let's solve the given equation step-by-step.
The equation we need to solve is:
[tex]\[ 7y - 2 \frac{3}{4} = \frac{1}{2} \][/tex]
Step 1: Convert the mixed fraction [tex]\( 2 \frac{3}{4} \)[/tex] to an improper fraction.
[tex]\[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \][/tex]
Step 2: Substitute the improper fraction back into the equation.
[tex]\[ 7y - \frac{11}{4} = \frac{1}{2} \][/tex]
Step 3: To eliminate the fraction, we can multiply every term by 4, the common denominator.
[tex]\[ 4 \left( 7y \right) - 4 \left( \frac{11}{4} \right) = 4 \left( \frac{1}{2} \right) \][/tex]
[tex]\[ 28y - 11 = 2 \][/tex]
Step 4: Add 11 to both sides to isolate the term with [tex]\( y \)[/tex].
[tex]\[ 28y = 2 + 11 \][/tex]
[tex]\[ 28y = 13 \][/tex]
Step 5: Divide both sides by 28 to solve for [tex]\( y \)[/tex].
[tex]\[ y = \frac{13}{28} \][/tex]
Therefore, the solution to the equation [tex]\( 7y - 2 \frac{3}{4} = \frac{1}{2} \)[/tex] is:
[tex]\[ y = \frac{13}{28} \][/tex]
