Q41. - Algebra 2

Question

Solve the equation. Check the solutions.

                       

$|a-3|-14=-6$

Step-by-Step Solution

Answer

The values are $a=11,-5$.

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Step 2- Simplify the expression.

Consider the expression $|a-3|-14=-6$.

 

Add 14 on both sides of the equation as follows:

$\begin{array}{l}|a-3|-14=-6\\ |a-3|-14+14=-6+14\\ |a-3|=8\end{array}$

Step 3- Step description.

Apply the absolute rule as follows:

 

Case 1. When $a-3=8$.

$\begin{array}{l}a-3=8\\ a=8+3\\ a=11\end{array}$

Case 2. When $a-3=-8$

$\begin{array}{l}a-3=-8\\ a=-8+3\\ a=-5\end{array}$

Therefore, the value is $a=11,-5$.

Step 4-Verify the solutions.

Substitute $a=11,-5$ in the equation $|a-3|-14=-6$ and simplify as follows:

$\begin{array}{l}|a-3|-14=-6\\ |11-3|-14=-6\\ \left|8\right|-14=-6\\ 8-14=-6\\ -6=-6\end{array}$

$\begin{array}{l}|a-3|-14=-6\\ |-5-3|-14=-6\\ |-8|-14=-6\\ 8-14=-6\\ -6=-6\end{array}$

Since the left-hand side and right-hand side is equal in both the cases thus the values are$a=11,-5$.