Algebra Unit 1 Review

Real Numbers and Algebraic Terms

100

When you add two rational numbers together, the answer will be _______

Rational

200

What is the constant in this expression:
2x-3y-6

-6

300

State whether the sum of these two numbers is rational or irrational. Explain why.

sqrt16 + sqrt8

The sum is irrational since 

sqrt16 = 4 , sqrt8=irrational, Rational+Irrational=Irrational

400

Create an expression that consists of three terms, a constant of 5, and a coefficient of -2

Example: -2x+3y+5

500

State whether the product of these numbers is rational or irrational. Explain why.

sqrt25 and sqrt144

Rational since 

sqrt25=5, sqrt144=12, 5times12=60

Properties of Real Numbers

100

Use the commutative property to rewrite the following expression so that the like terms are next to each other.

4+5x+6+2x+8x+3

4+6+3+5x+2x+8x or 5x+2x+8x+4+6+3

200

Use the distributive property to rewrite this expression without parentheses.

-2(4x-5)

-8x+10

300

Simplify the following expression

3(4x-2)+7

12x+1

400

Simplify the following expression

6-(2x+4)+x

-x+2

500

Simplify the following expression

3(x+1)-(-4x+3)

7x

Solving Equations

100

Solve this equation

x/4=5

x=20

200

Solve this equation

2x+3=9

x=3

300

Solve the equation

2(x+2)=14

x=5

400

Solve this equation

4+x/3+1=2

x= -9

500

Solve this equation

-2(3x+1)+4(-x+1)=22

x= -2

Variables on Both Sides and Absolute Value

100

What is the solution to this equation.

10-4x=-9x

x= -2

200

Solve the absolute value equation.

|x-5|=3

x=8 and x=2

300

What is the solution to this equation

4(x+3)=12+4x

Infinitely Many Solutions

400

What is the solution to this equation

1/2(8-6x)=8-3x

No solution

500

Solve the absolute value equation 

2|2x-4|-6=10

x=6 and x=-2

Literal Equations, Proportions, and Accuracy of Measure

100

Rewrite the literal equation for y 

x=yz

y=x/z

200

Solve the equation 

x/4=8/2

x=16

300

Solve the equation 

3/x=4/11

x=8.25

400

A picture has a length of 3.5 inches and a width of 1.7 inches. Your friend estimates the area of the picture to 5 inches squared. Did your friend accurately estimate the area of the picture? Why or why not. What would you estimate the picture to be? [Area=length x width]

No, 5 inches squared would be too small. You want to round up to 6 inches squared since the actual measurement is 5.95 inches squared.

500

Rewrite the literal equation for x

2/y =1/y + x/(a-b)

x=(a-b)/y