Solving Simple Equations
Proportions and Ratios
Solving equations with variables on both sides
Absolute Value Equations
Rewriting Equations and Formulas
100

`3w+7=19`

w = 4
100

`x/6 = 10/12`

x = 5

100

`15 - 2x = 3x`

x=3

100

Simplify

`|-3| + |3|`


6

100

Solve for y

`2x+y = 7`

`y = -2x + 7`

200

`(h+6)/5 = 2`

h = 4

200

`4/15 = x/27`

x = 7.2

200

`-3x + 10 = 15x - 8`

x = 1

200

Solve the equation

`|t/2| = 6`

t=6

200

Solve the literal equation for x.

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

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

300

`3.8 y + 5.6 y - 2 = 2.7`

y=0.5

300

`13/x = 5/4`

x = 10.4

300

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

x= -4

300

`2|-8w +6| = 76`

w = =4 

and 

w=5.5

300

Solve for y

`9x - y = 45`

`y = 9x - 45`

400

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

r = -6

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.

400

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

x = 1

400

`|x-1| + 5 = 2`

|x-1| = -3

NO SOLUTION

400

Rewrite to isolate F. 

`C = 5/9 (F - 32)`

`F = 9/5C + 32`

500

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

x = 5.5

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. 
500

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

5 = 4 

NO SOLUTION

500

`|3.5x| = 15.4`

x = 4.4

and 

x = 4.4

500

Solve the literal equation for x. 

`x - 9 + 2wx = y`

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