Chapter 8.2, Problem 50IP

To determine

The solution of the equation $0=t+4-9t$ , and check the solution.

Answer to Problem 50IP

  $t=0.5$

Explanation of Solution

Given:

The equation, $0=t+4-9t$ .

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 $0=t+4-9t$ for the unknown variable, isolate the variable term t on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate t on right side, first combining both the t terms and then subtract 4 from both sides and then divide both sides by -8 and then simplify further as shown below,

  $\begin{array}{l}0=t+4-9t\\ 0=-8t+4\\ 0-4=-8t+4-4\\ -4=-8t\\ \frac{-4}{-8}=\frac{-8t}{-8}\\ 0.5=t\end{array}$

Thus, the solution of the given equation is $t=0.5$ .

Now, to check the solution, substitute $t=0.5$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}0=t+4-9t\\ 0=0.5+4-9\left(0.5\right)\\ 0=0.5+4-4.5\\ 0=0\text{True Statement}\end{array}$

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