Solving Equations (ADV)

Literal Equations

100

Solve for m:

m - t = p

m = p + t

200

Solve for x:

xy = z

x = z/y

300

Solve for L

A = lwh

l = A/(wh)

400

Solve for b:

a^2+b^2=c^2

b=sqrt(c^2-a^2

500

Solve for w:

(5 + 12c)/w = 9

w = (5 + 12c) / 9

Compound Inequalities

100

-8 < c + 5 < -1

-13 < c < -6

200

a + 8 > -2 or -3a > -9

a > -10 or a < 3

300

12 ≤ 4n < 28

3 ≤ n < 7

400

2s + 3 ≥ 7  or 3s + 5 < 26

Infinite Solutions

500

-2> (3b+8)/2>13

No Solution

Graphing & Interval Notation

100

Graph the following inequality on a number line. d < 6

(-∞,6)

200

Graph the following inequality on a number line. w ≥ -2

[-2, ∞)

300

x ≥ 12 or x < -6

(-∞, -6) or [12, ∞)

400

x > -12 and x ≤ 20

(-12, 20]

500

Graph the following compound inequality. 8 ≤ s < 30

[8, 30)

Absolute Value Equations

100

|x| = 3

{-3,3}

200

|x/5| = 2

{-10, 10}

300

|-2x + 4| + 4 = 16

{-4, 8}

400

-3 |−8x| + 8 = 80

No Solution 

Ø

Absolute value cannot be set equal to a negative number (|-8x| = -24) because distance cannot be negative.

500

5+1/2|2x-4|=25

{-18, 22}

Multi-Step Equations

100

75 = 3(−6n − 5)

n = -5

200

2(n+1)=4n+1-2n

No Solution

Ø

300

9(y - 4) - 7y = 5(3y - 2)

y = -2

400

10p + 9 − 11 − p = −2(2p + 4) − 3(2p − 2)

p = 0

500

5-(v+4)=1/4(16v+4)-5v

Infinitely Many Solutions

∞