Chapter 8.2, Problem 21GP

To determine

The solution of the equation $1.1-t+2.2t=5.9$ , and check the solution.

Answer to Problem 21GP

  $t=4$

Explanation of Solution

Given:

The equation, $1.1-t+2.2t=5.9$ .

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 $1.1-t+2.2t=5.9$ 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 left side, first combining both the t terms and then subtract 1.1 from both sides and then divide both sides by 1.2 and then simplify further as shown below,

  $\begin{array}{l}1.1-t+2.2t=5.9\\ 1.1+1.2t=5.9\\ 1.1-1.1+1.2t=5.9-1.1\\ 1.2t=4.8\\ \frac{1.2t}{1.2}=\frac{4.8}{1.2}\\ t=4\end{array}$

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

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

  $\begin{array}{l}1.1-t+2.2t=5.9\\ 1.1-4+2.2\left(4\right)=5.9\\ 1.1-4+8.8=5.9\\ 5.9=5.9\text{True Statement}\end{array}$

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