Chapter 8.2, Problem 46IP

To determine

The solution of the equation $6=8.1-3x$ , and check the solution.

Answer to Problem 46IP

  $x=0.7$

Explanation of Solution

Given:

The equation, $6=8.1-3x$ .

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 $6=8.1-3x$ 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 right side, firstsubtract 8.1 from both sides and then divide both sides by -3 to simplify further as shown below,

  $\begin{array}{l}6=8.1-3x\\ 6-8.1=8.1-8.1-3x\\ -2.1=-3x\\ \frac{-2.1}{-3}=\frac{-3x}{-3}\\ 0.7=x\end{array}$

Thus, the solution of the given equation is $x=0.7$ .

Now, to check the solution, substitute $x=0.7$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}6=8.1-3x\\ 6=8.1-3\left(0.7\right)\\ 6=8.1-2.1\\ 6=6\text{True Statement}\end{array}$

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