Algebra 1 - Solving Equations

Simplifying expressions and Combining Like Terms

100

Simplify the following and combine like terms:

3(c+5)+2

3c+17

200

Simplify the following and combine like terms:

-3(x-8)

Answer:

-3x+24

300

Simplify the following and combine like terms:

3x²-2x+10-7x+5

Answer:

3x²-9x+15

400

Simplify the following and combine like terms:

3²+2(x+4)

Answer:

2x+17

500

Simplify the following and combine like terms:

5(x-4)+3(x+1)-7(x+2)

Answer:

x-31

Two-Step Equations

100

Solve for x:

2x + 3 = 15

(When you see it written 2x that means the same thing as 2*x)

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for a:

(1/2)a + 5 = 18

a = 26

WORK
(1/2)a + 5 = 18
(1/2)a + 5 - 5 = 18 - 5
(1/2)a = 13
2*(1/2)a = 13*2
a = 26

300

Solve for t:

-t + 8 = 3

t = 5

WORK
-t + 8 = 3
-t + 8 - 8= 3 - 8
-t = -5 [which is the same thing as -1t = -5]
-1t/-1=-5/-1
t = 5

400

Solve for x:

(x – 7)/3 = -12

x = -29

WORK
(x – 7)/3 = -12
3*((x – 7)/3)= -12*3
x – 7 = -36
x – 7 + 7= -36 + 7
x = -29

500

Solve for x:

-24 = -10x + 3

x = 2.7

WORK
-24 = -10x + 3
-24 - 3= -10x + 3 - 3
-27 = -10x
-27/(-10)=-10x/(-10)
2.7 = x

Multi-Step Equations

100

Solve for m:

5 = 5m - 23 + 2m

m =4

WORK
5 = 5m - 23 + 2m
5 = 5m + 2m - 23
5 = 7m - 23
5 + 23 = 7m - 23 + 23
28 = 7m
28/7 = 7m/7
4 = m

200

Solve for x:

(x + 4) + 2x = 67

x = 21

WORK
(x + 4) + 2x = 67
x + 2x + 4 = 67 [addition is commutative]
3x + 4 = 67
3x + 4 - 4= 67 - 4
3x = 63
3x/3 = 63/3
x = 21

300

Solve for x:

-8(2x - 1) = 36

x = -7/4

WORK
-8(2x - 1) = 36
-16x + 8 = 36 [Distributive Property]
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4

400

Solve for x:

3.5 - 0.02x = 1.24

x = 113

WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113

500

Solve for x:

3x/4 - x/3 = 10

[remember what fractions really look like?]

x = 24

WORK
3x/4 - x/3 = 10
9x/12 - 4x/12 = 10 [write fractions/common denominator]
5x/12 = 10
12*(5x/12) = 10*12
5x/5 = 120/5
x = 24

Random

100

What is Great Mill's Mascot?

The Hornet!

200

What is our Room Number?

A24

300

When are my office hours during Friday?

Must have the time they start and the time they end.

11:00AM-1:00PM

400

What is the code to access my office hours on Friday?

GMHSTAYLOR

500

How old is Mr. Taylor?

26 Years Old.

Parts of an Equation

100

Tell me the slope of the following line

y=-3x+10

The slope is -3.

200

What is the y-intercept of the following equation?

y+2=5x

The y-intercept is -2.

300

Given the following ordered pairs, calculate the slope of their line

(2,4)      (4,0)

slope formula=(y₂-y₁)/(x₂-x₁)

The slope is -2. 

400

We learned three different forms of a line. Tell me the form that the following line is written in.

3x-10y=12

Standard Form.

500

Given a line passes through the y intercept of -1, and goes through the points (1,2) and (3,8), what is the equation of the line in slope-intercept form?

y=3x-1