Answer :
Sure! Let's break down the problem and apply the distributive property step-by-step.
We have the equation:
[tex]\[
\frac{1}{3}(3q + 15) = 101
\][/tex]
1. Apply the Distributive Property: The distributive property tells us that we can multiply each term inside the parentheses by the factor outside the parentheses. Applying this, we get:
[tex]\[
\frac{1}{3} \times 3q + \frac{1}{3} \times 15
\][/tex]
2. Calculate Each Term:
- [tex]\(\frac{1}{3} \times 3q = q\)[/tex] because multiplying by [tex]\(\frac{1}{3}\)[/tex] and then by 3 cancels out the 3s, leaving q.
- [tex]\(\frac{1}{3} \times 15 = 5\)[/tex] because [tex]\(\frac{15}{3} = 5\)[/tex].
3. Rewrite the Equation:
Putting these terms together, the left side of the equation becomes:
[tex]\[
q + 5
\][/tex]
4. Form the New Equation: After simplifying using the distributive property, we get:
[tex]\[
q + 5 = 101
\][/tex]
The equation after correctly applying the distributive property is [tex]\(q + 5 = 101\)[/tex]. Therefore, among the given options, the correctly simplified equation is:
[tex]\(q + 5 = 101\)[/tex].
We have the equation:
[tex]\[
\frac{1}{3}(3q + 15) = 101
\][/tex]
1. Apply the Distributive Property: The distributive property tells us that we can multiply each term inside the parentheses by the factor outside the parentheses. Applying this, we get:
[tex]\[
\frac{1}{3} \times 3q + \frac{1}{3} \times 15
\][/tex]
2. Calculate Each Term:
- [tex]\(\frac{1}{3} \times 3q = q\)[/tex] because multiplying by [tex]\(\frac{1}{3}\)[/tex] and then by 3 cancels out the 3s, leaving q.
- [tex]\(\frac{1}{3} \times 15 = 5\)[/tex] because [tex]\(\frac{15}{3} = 5\)[/tex].
3. Rewrite the Equation:
Putting these terms together, the left side of the equation becomes:
[tex]\[
q + 5
\][/tex]
4. Form the New Equation: After simplifying using the distributive property, we get:
[tex]\[
q + 5 = 101
\][/tex]
The equation after correctly applying the distributive property is [tex]\(q + 5 = 101\)[/tex]. Therefore, among the given options, the correctly simplified equation is:
[tex]\(q + 5 = 101\)[/tex].
