Chapter 8.2, Problem 40IP

To determine

The solution of the equation $y-7y+6=30$ , and check the solution.

Answer to Problem 40IP

  $y=-4$

Explanation of Solution

Given:

The equation, $y-7y+6=30$ .

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 $y-7y+6=30$ 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 combining both the y terms and then subtract 6 from both sides and then divide both sides by -6 and then simplify further as shown below,

  $\begin{array}{l}y-7y+6=30\\ -6y+6=30\\ -6y+6-6=30-6\\ -6y=24\\ \frac{-6y}{-6}=\frac{24}{-6}\\ y=-4\end{array}$

Thus, the solution of the given equation is $y=-4$ .

Now, to check the solution, substitute $y=-4$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}y-7y+6=30\\ -6y+6=30\\ -6\left(-4\right)+6=30\\ 24+6=30\\ 30=30\text{True Statement}\end{array}$

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