Chapter 2: Q. 218 (page 240)

In the following exercise, solve the following equations with variables and constants on both sides.
$\frac{1}{4} y + 7 = \frac{3}{4} y - 3$

Short Answer

Expert verified

The solution for the given equation is $y = 20$

Step by step solution

Step 1. Given information

The given equation is $\frac{1}{4} y + 7 = \frac{3}{4} y - 3$

We have to solve the given equation

Step 2. Explanation

$\begin{array}{l} \Rightarrow \frac{1}{4} y + 7 = \frac{3}{4} y - 3 \\ \Rightarrow \frac{1}{4} y - \frac{3}{4} y + 7 = \frac{3}{4} y - \frac{3}{4} y - 3 (Subtract \frac{3}{4} yfromboththesides) \\ \Rightarrow \frac{1}{4} y - \frac{3}{4} y + 7 = - 3 (Simplify) \\ \Rightarrow \frac{1 y - 3 y}{4} + 7 = - 3 (TakeLCDtotheleftside)- \\ \Rightarrow - \frac{2 y}{4} + 7 = - 3 (Simplify) \\ \Rightarrow - \frac{1 y}{2} + 7 = - 3 (Simplify) \\ \Rightarrow - \frac{1 y}{2} + 7 - 7 = - 3 - 7 (Subtract7frombothsides) \\ \Rightarrow - \frac{1 y}{2} = - 10 (Simplify) \\ \Rightarrow - \frac{1 y}{2} \times (- 2) = - 10 \times (- 2) (Multiplyboththesidesby-2) \\ \Rightarrow y = 20 \\ Thesolutionisy=20 \end{array}$

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In the following exercise, solve the following equations with variables and constants on both sides.
$\frac{1}{4} y + 7 = \frac{3}{4} y - 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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In the following exercise, solve the following equations with variables and constants on both sides.
$\frac{1}{4} y + 7 = \frac{3}{4} y - 3$