Question

question 10 of 10
simplify: $7(v + 9) - 8(5 - 7v)$
a. $-28v - 10$
b. $-65 + v$
c. $63v + 23$
d. $40 - 100v$
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Explanation:

Step1: Distribute the coefficients

First, we distribute the 7 and -8 into the parentheses.
For \(7(v + 9)\), we get \(7v + 63\) (using the distributive property \(a(b + c)=ab + ac\), so \(7\times v = 7v\) and \(7\times9 = 63\)).
For \(-8(5 - 7v)\), we get \(-40 + 56v\) (using the distributive property \(a(b - c)=ab - ac\), so \(-8\times5=-40\) and \(-8\times(-7v)=56v\)).
Now the expression becomes \(7v + 63 - 40 + 56v\).

Step2: Combine like terms

Combine the \(v\)-terms: \(7v + 56v = 63v\).
Combine the constant terms: \(63 - 40 = 23\).
Putting it together, we have \(63v + 23\).

Answer:

C. \(63v + 23\)