Solution
- The question gives us the following expression to solve
[tex]5|x+1|=10[/tex]
- Before we proceed, we should get rid of the 5 multiplying the absolute value function. This would enable us to work directly with the absolute value function and make our work a lot easier.
- To get rid of the 5, we can simply divide both sides by 5. This is done below:
[tex]\begin{gathered} 5|x+1|=10 \\ \text{ Divide both sides by 5} \\ \\ \frac{5|x+1|}{5}=\frac{10}{5} \\ \\ |x+1|=2 \end{gathered}[/tex]
- Now, we can work directly with the absolute value function.
- The absolute value function has the property that
[tex]\begin{gathered} |x|=|-x|=x \\ \text{ That is, all negative numbers are made positive and positive numbers remain positive} \end{gathered}[/tex]
- We can apply this rule to the question. Based on what we have discussed so far, we can conclude that the number or expression (x + 1) inside the absolute value function can either be positive or negative and they would still give us a positive 2 as a result.
- Thus, we can say:
[tex]\begin{gathered} x+1=2 \\ \text{ OR} \\ x+1=-2 \\ \\ \text{ To be sure that these are the two possibilities, we can take the absolute value of both sides for the two} \\ \text{ expressionis} \\ That\text{ is,} \\ \\ |x+1|=|2|=2 \\ OR \\ |x+1|=|-2|=2 \end{gathered}[/tex]
- We can see that both expressions give us back the question. This means we just need to solve the two expressions and find the two possible values of x.
- This is done below:
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