Algebra Chapter 1 Review

Translating Equations

100

Write an equation that matches the phrase "five more than a number x is 12."

x+5=12

200

Translate to an equation: "Three times the sum of a number n and 4 equals 21."

3(n+4)=21

300

Translate: "The product of 7 and a number decreased by 2 equals 19"

7n-2=19

400

Create an equation: A gym charges a $25 sign-up fee plus $15 per month for membership. After several months, Sarah has paid a total of $100.

25+15x=100 

500

Write an equation from this real-world phrase: "A taxi charges a $3 base fare plus $2 per mile. If the total fare is F for m miles, write an equation relating F and m. Then write the equation when the total fare is $11."

F=3+2m

Solving Equations

100

Solve for Y: 3y - 5 = 16

y=7

200

Solve for Z: 

z/4 + 6=11

z=20

300

Solve for H: 

 24= 1/2h(4+6) 

(you will get a decimal)

h=4.8

400

Solve for P: 21=3p-6

p=9

500

Solve for P: 2/3p - 1/2 = 7/6

p=30/12 or 15/6 or 2 1/2 or 2.5

Variables on BOTH sides

100

5t=6(t-2)

t=12

200

4(x+9) = 6x-4

x=20

300

7x-12 = 3x+16

x=7

400

A movie theater charges different prices for adults and children. Five adult tickets cost $8 each, plus an $8 service fee. Two adult tickets cost $8 each, while 20 child tickets cost $1 each.

How many tickets would make the two costs equal?

Equation: 5x+8=2x+20 

x=4

500

James and Marcus are saving money. James currently has $8 more than 4 times the amount Marcus has. Marcus has $16 less than 6 times the amount James has.

How much money does each person have when their amounts are represented by the equation 4x + 8 = 6x - 16?

x=12

Absolute Value

100

Solve:  3|x+6|=30 

(remember you need 2 solutions)

x = -16, 4

200

A student is thinking of a number that is 7 units away from 3 on a number line.

(you should have 2 solutions)

Equation needed:  |x-3|=7 

Answers: -4, 10

300

Solve:  |3x-6| = 12 

(remember you need 2 solutions)

x = -2, 6

400

A thermometer is accurate to  +-5 degrees. Create an absolute value equation that can be used to find the highest and lowest temperatures if the thermometer is reading 19 degrees?

|x-19| = 5

500

Create an absolute value equation to represent the distance a football travels when thrown 17 yards from the 50-yard line. 

|x-50|=17

Proportions

100

 7/10 = m/14 

(you will get a decimal)

m= 9.8

200

 8/13 = v/21 

(you will get a decimal)

v=12.92

300

 x/3 = frac{3x+2}6 

x= -2

400

frac{x+15}10 = 8/5

x=1

500

frac{3}{x+4} = frac{2}{x-4}

x = 20

Rearranging Equations

100

Solve for F: 7f+g=5

f =  frac{5-g}{7} 

200

Solve for Y: x - 2y = 1

y =  frac{1-x}{-2} 

300

Solve for D: t=5d

d= 1/5d 

400

Solve for a: 6 + a/4 = 3

a = -12

500

Solve for d: frac{df+10}{6} = g 

d= frac{6g-10}{f}