Chapter 1.4, Problem 16PPSE

Solution

The solution of the equation $43-3d=d+9$ , and check the answer.

  $d=\frac{17}{2}$

Given:

The equation, $43-3d=d+9$ .

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to solve the given equation $43-3d=d+9$ , isolate the variable on left side by performing the basic algebraic operations as shown below

  $\begin{array}{c}43-3d=d+9\\ 43-3d-d=d-d+9\\ 43-4d=9\\ 43-43-4d=9-43\\ -4d=-34\\ \frac{-4d}{-4}=\frac{-34}{-4}\\ d=\frac{17}{2}\end{array}$

Thus, the solution of the equation is $d=\frac{17}{2}$ .

To check the answer, substitute $d=\frac{17}{2}$ into the given equation and show that the left-hand side expression is equal to the right-hand side expression as shown below

  $\begin{array}{c}43-3d=d+9\\ 43-3\cdot \frac{17}{2}=\frac{17}{2}+9\\ 43-\frac{51}{2}=\frac{17+18}{2}\\ \frac{86-51}{2}=\frac{35}{2}\\ \frac{35}{2}=\frac{35}{2}\text{True statement}\end{array}$