Chapter 1.9, Problem 21PPE

To determine

The solution of the equation $\frac{2}{3}+w=1\frac{1}{2}$ , and check the solution.

Answer to Problem 21PPE

  $w=\frac{5}{6}$

Explanation of Solution

Given:

The equation, $\frac{2}{3}+w=1\frac{1}{2}$ .

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 $\frac{2}{3}+w=1\frac{1}{2}$ for the unknown variable, isolate the variable term w on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate w on left side, first subtract $\frac{2}{3}$ from both sides and then simplify further by taking the Least Common Denominator (LCD) and solve further as shown below,

  $\begin{array}{c}\frac{2}{3}+w=1\frac{1}{2}\\ \frac{2}{3}+w-\frac{2}{3}=1\frac{1}{2}-\frac{2}{3}\\ w=\frac{3}{2}-\frac{2}{3}\\ w=\frac{9}{6}-\frac{4}{6}\\ w=\frac{9-4}{6}\\ w=\frac{5}{6}\end{array}$

Thus, the solution of the given equation is $w=\frac{5}{6}$ .

Now, to check the solution, substitute $w=\frac{5}{6}$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{c}\frac{2}{3}+w=1\frac{1}{2}\\ \frac{2}{3}+\frac{5}{6}=1\frac{1}{2}\\ \frac{4}{6}+\frac{5}{6}=\frac{3}{2}\\ \frac{4+5}{6}=\frac{3}{2}\\ \frac{9}{6}=\frac{3}{2}\\ \frac{3}{2}=\frac{3}{2}\text{True Statement}\end{array}$

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