Chapter 2.2, Problem 6P

Solve each equation. Check your answer.

$13=8-5d$

To determine

To solve the equation:

  $13=8-5d$

And also check the solution.

Answer to Problem 6P

  $d=-1$

Explanation of Solution

Given:

  $13=8-5d$

Concept Used:

• Steps to solve a linear equation:
1. Use distributive property to remove any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variable terms on one side of the equation and the constant on the other side.
4. Isolate the variable
• To check the solution of a equation substitute the solution in the equation and check whether it satisfies.

Calculation:

In order to solve the equation:

  $13=8-5d$

Isolate the variable by subtracting 8 from both sides, as

  $\begin{array}{c}13=8-5d\\ \Rightarrow 13-8=8-5d-8\\ \Rightarrow 5=-5d\end{array}$

Now divide both side by $-5$

  $\begin{array}{c}5=-5d\\ \Rightarrow \frac{5}{-5}=\frac{-5d}{-5}\\ \Rightarrow -1=d\\ \Rightarrow d=-1\end{array}$

Thus, solution of given equation is $d=-1$ .

Now, to check this solution put $d=-1$ in right hand side of the given equation, and check whether both sides are equal. As,

  $\begin{array}{c}8-5\times \left(-1\right)=8+5\\ =13\\ =\text{Left hand side}\end{array}$

Thus, $d=-1$ is correct solution for given equation.