Answer:
Equation: [tex]\frac{1}{2}[/tex]n - 7 = 3n - 33
Answer: n = 10.4
Step-by-step explanation:
Using key words from the verbal description, you can set up an equation to solve for the missing variable. Start with one part of the description at a time: '7 less than half a number'. Half a number = [tex]\frac{n}{2}[/tex] or [tex]\frac{1}{2}[/tex]n. '7 less than' means we have to subtract 7 from that number: [tex]\frac{1}{2}[/tex]n - y. 'Is equal' is our '=' sign. Next, 33 less than three times the number. 'Three times a number' = 3n. '33 less than' means we have to subtract 33 from 3n: 3n - 33. Put them together:
[tex]\frac{1}{2}[/tex]n - 7 = 3n - 33
Use inverse operations to solve by adding 33 to both sides:
[tex]\frac{1}{2}[/tex]n - 7 + 33 = 3n - 33 + 33 or [tex]\frac{1}{2}[/tex]n + 26 = 3n
Use inverse operations to subtract [tex]\frac{1}{2}[/tex]n from both sides:
[tex]\frac{1}{2}[/tex]n + 26 - [tex]\frac{1}{2}[/tex]n = 3n - [tex]\frac{1}{2}[/tex]n
Combine like terms: 26 = 2.5n, then divide both sides by 2.5: 26/2.5 = 2.5n/2.5.
n = 10.4
