Chapter 1.1, Problem 13E

To determine

To solve the equation

  $r+\left(-8\right)=10$

Answer to Problem 13E

  $r=18$ is the solution.

Explanation of Solution

Given: Equation: $r+\left(-8\right)=10$

Formula Used:

The addition property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.

Calculation:

Given: Equation: $r+\left(-8\right)=10$

To solve the equation, bracket is opened first

  $\begin{array}{l}r+\left(-8\right)=10\\ r-8=10\end{array}$

Adding $8$ to both the sides as “Addition property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.”

  $\begin{array}{l}r-8+8=10+8\\ r=18\end{array}$

Thus, the solution is $r=18$ .

Now, putting the value of $r=18$ in the L.H.S. of the equation, we have:

  $\begin{array}{l}18+\left(-8\right)=18-8\\ 18+\left(-8\right)=10\end{array}$

And R.H.S. of the equation is $10$ .

Hence, L.H.S. $=$ R.H.S.

Thus, the solution is correct.

Conclusion:

Hence, the solution is $r=18$ .