Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. 10(5v + 2) = 9v + 20 50v + 20 = 9v + 20 □ + 20 = 20 subtract 9v from both sides 41v = 0 v = □ divide both sides by 41

Explanation:

Step1: Identify the first missing description

The step from \(10(5v + 2)=9v + 20\) to \(50v + 20 = 9v + 20\) is done by using the distributive property (multiplying 10 with each term inside the parentheses: \(10\times5v = 50v\) and \(10\times2 = 20\)). So the first missing description is "Distribute the 10 (or Use the distributive property)".

Step2: Find the missing term after subtracting \(9v\)

We have \(50v+20 = 9v + 20\). Subtract \(9v\) from both sides: \(50v-9v+20=9v - 9v+20\), which simplifies to \(41v + 20=20\). So the missing term is \(41v\).

Step3: Identify the missing description for getting \(41v = 0\)

We have \(41v+20 = 20\). To get \(41v=0\), we subtract 20 from both sides. So the missing description is "Subtract 20 from both sides".

Step4: Solve for \(v\)

We have \(41v = 0\). Divide both sides by 41: \(v=\frac{0}{41}=0\).

Answer:

• First missing description: Distribute the 10 (or Use the distributive property)
• Missing term: \(41v\)
• Second missing description: Subtract 20 from both sides
• Value of \(v\): \(0\)

(In the table format as per the problem's requirement, filling the blanks:

• First dropdown: Distribute the 10 (or Use the distributive property)
• First box: \(41v\)
• Second dropdown: Subtract 20 from both sides
• Second box: \(0\))