To clear the fractions in the given equation and simplify it, follow these steps:
1. Start with the given equation:
[tex]\[
\frac{2y}{3} - \frac{1}{6} = \frac{7}{2}
\][/tex]
2. Identify a common multiple for the denominators 3, 6, and 2. The least common multiple (LCM) of these denominators is 6.
3. Multiply every term in the equation by 6 to clear the fractions:
[tex]\[
6 \left(\frac{2y}{3}\right) - 6 \left(\frac{1}{6}\right) = 6 \left(\frac{7}{2}\right)
\][/tex]
4. Simplify each term:
[tex]\[
\left(6 \div 3\right) \cdot 2y - \left(6 \div 6\right) \cdot 1 = (6 \div 2) \cdot 7
\][/tex]
This reduces to:
[tex]\[
2 \cdot 2y - 1 = 3 \cdot 7
\][/tex]
Further simplification gives us:
[tex]\[
4y - 1 = 21
\][/tex]
Therefore, the step to clear the fractions is to multiply both sides of the equation by 6, and the resulting equation is:
[tex]\[
4y - 1 = 21
\][/tex]
