Question

Solve each of the following equations and check your answers:
$2y-\frac{1}{2}=-\frac{1}{3}$

Answer 1

2y − $\frac{1}{2}$$$$=-\frac{1}{3}$
Adding $\frac{1}{2}$$$to both sides, we get
⇒ 2y − $\frac{1}{2}$$+$$\frac{1}{2}$$$$=-\frac{1}{3}$ + $\frac{1}{2}$$$
⇒ 2y = $\frac{-2+3}{6}$
⇒ 2y = $\frac{1}{6}$$$
Dividing both sides by 2, we get
⇒ $\frac{2y}{2}=\frac{1}{6\times 2}$
⇒ y = $\frac{1}{12}$
Verification:
Substituting y = $\frac{1}{12}$ in LHS, we get
LHS = $2\times \left(\frac{1}{12}\right)-\frac{1}{2}=\frac{1}{6}-\frac{1}{2}$ =$\frac{1-3}{6}=\frac{-2}{6}$ =$-\frac{1}{3}$, and RHS = $-\frac{1}{3}$
LHS = RHS
Hence, verified.