Solving Linear Functions, Equations, and Inequalities

Solving Equations

100

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

Solve for x. 

x = -6

200

2(x + 5) - 7 = 3(x - 2)

Solve for x.

x = 9

300

Solve for n.

-16 + 7n + n = 8n + 4n

n = -4

400

Solve for k.

12k +15 = 35 +2k

k = 2

500

What is the first step in solving multi-step equations?

Distribute and combine like terms.

Solving Inequalities

100

5(-5 - 8n) + 1 > 12 + 4n

what is the solution for n?

n < -9/11

200

What is the solution for x?

6x - 2(x - 7) > 6(x +3)

x < -2

300

What should we do, in solving inequalities, when we divide or multiply by a negative coefficient?

Flip the inequality sign.

400

When graphing the inequality statement on a number line, what symbols require a close circle?

The greater than/equal to or less than/equal to.

Literally Literal Equations

100

What are literal equations?

Equations with two or more variables.

200

Solve for y.

8x + 4y = 16

y = 4 - 2x or y = -2x +4

300

Solve for R.

pV = nRT

R = pV/nT

400

Solve for s.

D = C - s/n

s = C - Dn or s = -Dn + C

500

The area of a triangle can be found using the equation: A = 1/2bh. Write an equation that solves for b in terms of A.

b = 2A/h

Arithmetic Sequences

100

What is the constant difference in the sequence below?

               97, 86, 75, 65, ...

-11

200

What is the next term in the sequence?

          4, 7, 10, 13,...

16

300

Write the explicit formula for the sequence:

                  2, 8, 14, ...

(Hint: simplify the equation)

a_n = 6n - 4

400

What is the 32nd term in this sequence?

                   9, 4, -1, -6, -11

a₃₂ = -146

500

Write the explicit formula for the sequence, then find the 20th term. (Hint: simplify the equation)

                 5, 12, 19, 26, ...

a_n = 7n - 2

   a₂₀ = 138

Throwback

100

Is this a relation a function?

(2, 3), (4, 9), (3, 8), (4, 15)

No

200

For the function {(0,1), (1,-3), (2, -4), (-4,1)}, write the domain and range.

D: {-4,0,1,2}

R: {-4, -3, 1}

300

Evaluate f(4) if f(x) = x² -5x.

f(4) = -20

400

Evaluate f(-2) if f(x) = x² + 3.

f(-2) = 7

500

Evaluate h(-4) if h(x) = 2h² - 4h +2.

h(-4) = 50