Chapter 1.9, Problem 20PPE

To determine

The solution of the equation $-\frac{1}{4}=\frac{2}{3}b$ , and check the solution.

Answer to Problem 20PPE

  $b=-\frac{3}{8}$

Explanation of Solution

Given:

The equation, $-\frac{1}{4}=\frac{2}{3}b$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $-\frac{1}{4}=\frac{2}{3}b$ for the unknown variable, isolate the variable term b on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate b on right side, first multiply both sides by the reciprocal $\frac{3}{2}$ to get rid of the fraction with it and then simplify further as shown below,

  $\begin{array}{c}-\frac{1}{4}=\frac{2}{3}b\\ -\frac{1}{4}\cdot \frac{3}{2}=\frac{2}{3}b\cdot \frac{3}{2}\\ -\frac{3}{8}=b\end{array}$

Thus, the solution of the given equation is $b=-\frac{3}{8}$ .

Now, to check the solution, substitute $b=-\frac{3}{8}$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{c}-\frac{1}{4}=\frac{2}{3}b\\ -\frac{1}{4}=\frac{2}{3}\cdot \\ \frac{30}{5}=6\\ 6=6\text{True Statement}\end{array}$

Since, the left hand side and right hand side are equal, so the solution is correct.