Module 5: Creating Linear Equations

The sum of n and 5 is five less than fifteen.

• n+5=15+5

• x+5=15-5

• n-5=15+5

• n+5=15-5

• 5n=75

The difference of y and four is equal to sixteen.

• y-4=16

• 4-y=16

• 16-4=y

• 4-16=y

• y/4=16

Four times the sum of two and a number is equal to the product of a number and five.

• 4(2+x)=(5y)

• 8+x=(5y)

• 42+x=5y

• 4(2x)=(5y)

• 4(2+x)=(5+y)

A​ town's population is 47,500. About 75 people move out of the town each month. Each​ month, 125 people on average move into town. A nearby town has a population of 50,250. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be​ equal? Write an equation to model the situation. Then solve the equation and answer the question.

• 125m-75m+50,250=47,500-200m

• 75m-125m+ 50,250 = 47,500-200m

• 75m-125m+47,500 = 50,250-200m

• 125m-75m+47,500 = 50,250-200m

Rayshawn and Robert are both saving money for their summer vacations. They began saving at the same time. Rayshawn started with $10.25 and adds $5.15 to his savings every month. Robert did not have a starting amount but adds $10.25 to his savings every month. Which equation could be used to determine how many months, m, it will take before Rayshawn and Robert both have saved the same amount of money?

• 5.15m + 10.25 = 10.25m

• 10.25m + 5.15 = 10.25m

• 10.25m + 10.25 = 5.15m

• 10.25m – 5.15 = 10.25m

82 added to a number is the same as 36

• 82=36

• 82+36=x

• t+82=36

• None of the above

The product of 12 and a number is the same as 2 removed from a number

• 12x=x+2

• 12x=2-x

• 12-2=x-2

• 12x= x-2

a number halved is equal to 22 fewer than a number

• b⁄2 = 22-b

• 2b =22- b

• n⁄2=n-22

• None of the above

120 more than twice a number is the same as halve a number removed from 8

• 2t+120= t⁄2-8

• 120+2t = t⁄2-8

• 2t+120 = 8-t⁄2

• Be humble...sit down