Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -5(12v - 8) + 7v = -12v - 1 -60v + 40 + 7v = -12v - 1 apply the distributive property -53v + 40 = -12v - 1 dropdown -41v + 40 = -1 add -60v to both sides subtract -60v from both sides multiply both sides by -60v divide both sides by -60v combine like terms -41v = -41 v = 1 dropdown

Explanation:

Step1: Distribute -5 to parentheses

$-5(12v - 8) + 7v = -12v - 1$
$\implies -60v + 40 + 7v = -12v - 1$

Step2: Combine like v terms

$-60v + 7v = -53v$, so:
$-53v + 40 = -12v - 1$

Step3: Add 53v to both sides

$-53v + 53v + 40 = -12v + 53v - 1$
$\implies 40 = 41v - 1$
$\implies -41v + 40 = -1$

Step4: Subtract 40 from both sides

$-41v + 40 - 40 = -1 - 40$
$\implies -41v = -41$

Step5: Divide by -41 on both sides

$\frac{-41v}{-41} = \frac{-41}{-41}$
$\implies v = 1$

Answer:

1. Missing term after 40: (no term needed, the blank is just the result of distribution, the correct action here is "Apply the distributive property")
2. Missing description for $-53v + 40 = -12v - 1$: Combine like terms
3. Missing term for $-41v + 40 = -1$: (derived by adding 53v to both sides, the final filled values are)

• Blanks filled: $40$, $-53v$, $-41v$, $-41$, $1$
• Selected descriptions: "Apply the distributive property", "Combine like terms", "Add 53v to both sides (equivalent to the step leading to $-41v + 40 = -1$)", "Subtract 40 from both sides", "Divide both sides by -41"

Final solved value: $v=1$