Question

question 1-8
doubling the sum of rob’s and cheryl’s ages gives 38. if cheryl is 10 years old, how old is rob?
the equation that can be used to solve this is
this means that rob is
years old.
2x + 10 = 38
2x − 10 = 38
10x + 2 = 38
10x − 2 = 38
2(x + 10) = 38
2(x − 10) = 38
10(x + 2) = 38

Explanation:

Step1: Analyze the equation

We are given the equation \(10x - 2=38\) (assuming this is the correct equation from the options, likely representing the relationship between Rob's age \(x\) and the doubling of the sum of their ages). First, we need to isolate the term with \(x\).
Add 2 to both sides of the equation:
\(10x- 2 + 2=38 + 2\)
\(10x=40\)

Step2: Solve for \(x\)

Divide both sides of the equation \(10x = 40\) by 10:
\(x=\frac{40}{10}\)
\(x = 4\)? Wait, no, maybe the equation is \(2(x + 10)=38\) (since Cheryl is 10, sum of ages is \(x + 10\), doubling it is \(2(x + 10)\)). Let's re - evaluate. If the correct equation is \(2(x + 10)=38\) (since doubling the sum of Rob's age \(x\) and Cheryl's age 10 gives 38).

Step1 (corrected): Start with the correct equation

Given the problem: Doubling the sum of Rob's (\(x\)) and Cheryl's (10) ages gives 38. So the equation is \(2(x + 10)=38\)
Divide both sides by 2:
\(\frac{2(x + 10)}{2}=\frac{38}{2}\)
\(x + 10 = 19\)

Step2 (corrected): Solve for \(x\)

Subtract 10 from both sides:
\(x+10 - 10=19 - 10\)
\(x = 9\)

Wait, maybe the equation from the options is \(2(x + 10)=38\). Let's check the options again. The options include \(2(x + 10)=38\). Let's solve this equation properly.

Step1: Divide both sides by 2

Given \(2(x + 10)=38\), divide both sides by 2:
\(x + 10=\frac{38}{2}=19\)

Step2: Subtract 10 from both sides

\(x=19 - 10 = 9\)

Answer:

Rob is 9 years old.