Download Algebra 2 unit 1 solving

Solving 2 step equations
1.
2.
3.
4.
Oppositeof what the equation says
Do the _________
Do the ___________to
Same steps both sides of =
Use ______________
order of operations
Backwards
Justify your work!
Mult. or Divide
Add or Subtract BEFORE _________________
________________
3x + 8 = 23
-8 -8 sub prop =
3x
= 15
3
3 div prop 2*
=
X = 5 mult id
H - 4 = 7
2
+4 +4 add prop =
H
=11 *2 mult pr =
2 1H = 22 mult id
H = 22
Jim buys 3 shirts and a pair of jeans for $50.
The jeans cost $23. Write and equation to
find the cost of each shirt.
3 s + J = 50
3 s + 23 = 50
-23
3s
3
-23 sub prop =
= 27
3 div prop =
s
= 9 mult id
Cost of each shirt is $9
Solving multi- step equations
Like Terms by adding them together.
1. Combine __________
Variables on one side of the =.
2. Get all the ___________
Numbers on the OTHER side.
3. Get all the ___________
Change the Sign
Cross the line and
To finish solving, usually ___________
Divide
3x + 8 + 2x = 23
5x + 8 = 23
5x = 15
5
5
X=3
5T – 4 = 3T + 8
5T -3T -4 = 8
2T -4 = 8
2T = 8 +4
2T = 12
2 2
T=6
x Solve for x if the
perimeter is 33
3x+4
3x+1 + 3x+4 + x = 33
3x+1 + 3x +4 + x = 33
7x + 5 = 33
7x = 33 - 5
7x = 28
7 7
X=4
3x+1
Solve for X
6x + 7
4x-9
6x + 7 = 4x - 9
6x – 4x + 7 = -9
2x + 7 = -9
-7 -7
2x = -16
X = -8
Solving Inequalities
Symbols
Rules
Example
Example
Greater Than
>
Greater Than or equal
>
Less Than
<
Less Than or equal
<
Solve just like an equation, but check which way
The inequality is going.
MULTIPLYING OR DIVIDING BY A
NEGATIVE (-) SWITCHES THE INEQUALITY!
X+8 > 10
-8 -8
X>2
2x+7 < 3
-7 -7
2x < -4
2
2
x < -2
-4X – 1 < 11
0 1 2 3 4
-4 -3 -2 -1 0 1
-3 -2 -1 0 1 2 3
Solving Inequalities
Greater Than
>
Less Than <
Greater Than or equal
Less Than or equal
P7
>
<
Solve just like an equation, but check which way the inequality goes.
MULTIPLYING OR DIVIDING BY A NEGATIVE (-)
SWITCHES THE INEQUALITY!
EX #1: X+8 > 10
X+8 > 10
-8 -8
X>2
EX #3: -4X – 1<11
-4X – 1 < 11
+1 +1
-4x < 12
-4 -4
0 1 2 3 4
ANY number greater
than 2 makes this true!
EX #2: 2X + 7 < 3
2x+7 < 3
-7 -7
2x < -4
2
2
x < -2
X > -3 SWITCH the sign!!
-4 -3 -2 -1 0 1
ANY number less than or
equal -2 makes this true!
-3 -2 -1 0 1 2 3
Solving Literal Equations
Literal
Equation
Solving
Regular
Equation
An equation with more than 1 variable.
Often a formula
To SOLVE a literal equation, get one variable by itself.
Show the regular solving steps, but
DON’T DO THE MATH!
3 X + 5 = 14
-5 -5 Subtract the 5 : sub property
3x = 14-5
/3
/ 3 Divide by 3 : division property
X = (14-5)/3 = 9/3 = 3
Literal
Equation
4X + 6Y = W
-6Y -6Y Subtract the 6 : sub property
4x = W-6Y
/ 4 / 4 Divide by 4 : division property
X = W-6Y
4
5 = (3N)
4
*4 *4
mult prop
20 = 3N
/3 /3
div prop
20/3 = N
A = (HB) Solve for B
2
*2 *2 mult prop
2A = H*B
/H /H div prop
2A/H = B