Chapter 8.2, Problem 37IP

To determine

The solution of the equation $\frac{1}{8}y-\frac{1}{2}=\frac{7}{8}$ , and check the solution.

Answer to Problem 37IP

  $y=11$

Explanation of Solution

Given:

The equation, $\frac{1}{8}y-\frac{1}{2}=\frac{7}{8}$ .

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 $\frac{1}{8}y-\frac{1}{2}=\frac{7}{8}$ for the unknown variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate y on left side, first add 1/2 both sides and then multiply both sides by 8 and then simplify further as shown below,

  $\begin{array}{l}\frac{1}{8}y-\frac{1}{2}=\frac{7}{8}\\ \frac{1}{8}y-\frac{1}{2}+\frac{1}{2}=\frac{7}{8}+\frac{1}{2}\\ \frac{1}{8}y=\frac{11}{8}\\ \frac{1}{8}y\times 8=\frac{11}{8}\times 8\\ y=11\end{array}$

Thus, the solution of the given equation is $y=11$ .

Now, to check the solution, substitute $y=11$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}\frac{1}{8}y-\frac{1}{2}=\frac{7}{8}\\ \frac{1}{8}\left(11\right)-\frac{1}{2}=\frac{7}{8}\\ \frac{11}{8}-\frac{1}{2}=\frac{7}{8}\\ \frac{11-4}{8}=\frac{7}{8}\\ \frac{7}{8}=\frac{7}{8}\text{True statementy}\end{array}$

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