Algebra 1: Chapter 1 Test Prep

Solving Simple Equations

100

3w+7=19

w = 4

200

(h+6)/5 = 2

h = 4

300

3.8 y + 5.6 y - 2 = 2.7

y=0.5

400

5(r+9) -2(1-r) = 1

r = -6

500

83.8 = 8.6x-7.3(6-2x)

x = 5.5

Proportions and Ratios

100

x/6 = 10/12

x = 5

200

4/15 = x/27

x = 7.2

300

13/x = 5/4

x = 10.4

400

A painter needs to reach the top of a wall using a ladder. The right triangles formed by the objects and their shadows are similar. The ladder is placed 12 feet away from the base of the wall. The painter is 5 feet tall and casts a shadow of 3 feet. The painter has a ladder that can reach up to 20 feet. Can the painter use the ladder to reach the top of the wall?

h = 20 feet.

Yes, the painter can use the ladder to reach the top using the ladder.

500

An enterpreneur wants to rent a billboard at least 30 feet tall to display an advertisement for her business. She is 5 feet 6 inches tall and casts a shadow of 7 feet. At the same time, a billboard casts a shadow of 35 feet. Is the billboard tall enough?

No. She wants the billboard to be 30 feet tall yet the height is only 27.5 feet tall. 

Solving equations with variables on both sides

100

15 - 2x = 3x

x=3

200

-3x + 10 = 15x - 8

x = 1

300

10(x + 5) = 2(x+9)

x= -4

400

2(2x+4)=3/4(24-8x)

x = 1

500

5(1+2m) = 1/2(8+20m)

5 = 4 

NO SOLUTION

Absolute Value Equations

100

Simplify

|-3| + |3|

6

200

Solve the equation

|t/2| = 6

t=6

300

2|-8w +6| = 76

w = =4 

and 

w=5.5

400

|x-1| + 5 = 2

|x-1| = -3

NO SOLUTION

500

|3.5x| = 15.4

x = 4.4

and 

x = 4.4

Rewriting Equations and Formulas

100

Solve for y

2x+y = 7

y = -2x + 7

200

Solve the literal equation for x.

x = (y-12)/(-5-4k)

x = (y-12)/(-5-4k)

300

Solve for y

9x - y = 45

y = 9x - 45

400

Rewrite to isolate F. 

C = 5/9 (F - 32)

F = 9/5C + 32

500

Solve the literal equation for x. 

x - 9 + 2wx = y

x = (9+ y) / (1+2w)