Chapter 2: Q. 2.99 (page 258)

$Solve:x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2}$

Short Answer

Expert verified

$Thesolutionforthegivenequationisx=-1$

Step by step solution

Step 1. Given information

The given equation is $x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2}$

We have to solve the given equation.

Step 2. Explanation

$\begin{array}{l} Solve:x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2} \\ \Rightarrow x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2} (FindtheLCDofallfractionsintheequation) \\ TheLCDis6. \\ \Rightarrow 6 \times (x+ \frac{1}{3})= 6 \times (\frac{1}{6} x- \frac{1}{2})(MuliplybothsidesoftheequationbytheLCD6) \\ \Rightarrow 6 \times x+ 6 \times \frac{1}{3} = 6 \times \frac{1}{6} x- 6 \times \frac{1}{2} (Distribute) \\ \Rightarrow 6 x + 2 =x-3(Simplify) \\ \Rightarrow 6 x -x+ 2 =x-x-3(Subtractxfrombothsides) \\ \Rightarrow 5 x + 2 =-3(Simplify) \\ \Rightarrow 5 x + 2 - 2 =-3 - 2 (Subtract2frombothsides) \\ \Rightarrow 5 x =-5(Simplify) \\ \Rightarrow \frac{5 x}{5} = \frac{-5}{5} (Dividebothsidesby5) \\ \Rightarrow x = - 1 \\ Thesolutionforthegivenequationisx=-1 \end{array}$

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$Solve:x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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$Solve:x+ \frac{1}{3} = \frac{1}{6} x- \frac{1}{2}$