Chapter 8.2, Problem 39IP

To determine

The solution of the equation $46-8x=-18$ , and check the solution.

Answer to Problem 39IP

  $x=8$

Explanation of Solution

Given:

The equation, $46-8x=-18$ .

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 $46-8x=-18$ for the unknown variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first subtract 46 from both sides and then divide both sides by -8 and then simplify further as shown below,

  $\begin{array}{l}46-8x=-18\\ 46-46-8x=-18-46\\ -8x=-64\\ \frac{-8x}{-8}=\frac{-64}{-8}\\ x=8\end{array}$

Thus, the solution of the given equation is $x=8$ .

Now, to check the solution, substitute $x=8$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}46-8x=-18\\ 46-8\left(8\right)=-18\\ 46-64=-18\\ -18=-18\text{True statementy}\end{array}$

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