Download METHOD 1: Solving One-Step Equations by Inspection

9.1 Solve Equations
We are going to learn four different methods for solving equations.
METHOD 1: Solving One-Step Equations by Inspection
We will use inspection to solve for the variable (unknown).
a) If we are given x + 3 =
What number added to 3 is equal to 9?
That number is ______
So we can say x = _______
b) If we are given x - 2 = 7
What number, less 2, will be equal to 7?
That number is ______
c) If we are given 4x = -20
So we can say x = _______
***REMEMBER 4x is “4 times x”
What number multiplied by 4 equals -20?
That number is ______
So we can say x = _______
d) If we are given x ÷ 3 = 5
What number divided by 3 gives 5?
That number is ______
So we can say x = _______
METHOD 2: Solve Using Systematic Trial
What number multiplied by 7, less 2, equals 166?
Value (guess)
20
30
25
24
Equation 7x – 2 = 166
True or False
Therefore, the solution is x = _________
Now let’s try the cover-up method. This method is a more efficient way
to help you solve by inspection.
METHOD 3: Cover-Up Method
Solve:
2x + 4 = 10
Step 1: Cover up the 2x.
2x + 4 = 10
What value for 2x makes this true?
+ 4 = 10
6 makes the equation true.
6
+ 4 = 10
2 times a number gives 6. What is the number?
This means that 2x must be
equal to 6.
Step 2: Now cover up the x only
3 makes the equation true.
Therefore, x = 3 is the solution.
2x = 6
2
=6
METHOD 4: Solve Using Models
Refer to Example 4 on Page 376.
Work through examples a, b, and c
Homework:
Solving Equations Worksheet
Page 379 # 1, 2, 3, 4, 5, 6, 7, 9
Page 380 # 10, 11, 12, 13, 14, 15, 16 PASS IN #17
Solving Equations Worksheet
Answer the following questions in your binders or scribblers.
Solve the following by Inspection or the Cover-Up Method:
x
= 25
2
1) a + 4 = 12
2) x – 3 = 10
3) – 2 = x + 1
4)
5) 60 = -6z
6) x – 6 = 10
7) x – 2 = - 2
8) 2x = 80
9) -22 = 11y
10) x + 16 = 2
11) X + 2 = 12
12)
14) -99 + x = 1
15) x – 21 = 36
16) 4x = 48
13) 6 =
y
6
Solve the following by Modeling:
1)
2)
3)
4)
5)
6)
7)
8)
9)
y
= 16
2
Solving One-Step Equations
Use the inverse operation (opposite operation) that is displayed to determine what
value the variable has.
DON”T FORGET: Any operation performed to one side must be performed to the
other side of the equal sign.
REMEMBER: ZERO PRINCIPAL:
-8+8=0
+3 + (-3) = 0
Example 1:
x+6=8
x+6– 6=8– 6
x=2
The variable “x” is not alone on one side of
the equal sign,
6 is being added to it.
Perform the inverse operation to both sides, which
means subtract 6 from both sides.
Example 2:
x-8=4
The variable “x” is not alone on one side of
x - 8 + 8 = 4 + 8 the equal sign,
x = 12
8 is being subtracted from it.
Perform the inverse operation to both sides, which
means add 8 from both sides.
Example 3:
5x = -35
5x = -35
5
5
The variable “x” is not alone on one side of
the equal sign,
It is being multiplied by 5.
Perform the inverse operation to both sides to isolate
the variable.
Divide both sides of the equation by 5.
Example 4:
The variable “x” is not alone on one side of
the equal sign,
It is being divided by 3.
Perform the inverse operation to both sides to isolate
the variable.
Multiply both sides of the equation by 3.
Solving Equations Worksheet
Part A: Solve the following addition equations. SHOW YOUR WORK
x + 8 = 13
x + 5 = 15
21 + y = 24
4 + y = 12
12 + y = 16
x + 9 = 15
Part B: Solve the following subtraction equations. SHOW YOUR WORK
y - 15 = 25
y – 19 = 15
1-x=4
4 - x = 12
2-y=6
x-3=5
Part C: Solve the following division equations. SHOW YOUR WORK
x
= 21
7
x
= 15
3
y
= 10
4
y
= 24
6
x
= 25
8
y
= 72
6
Part D: Solve the following multiplication equations. SHOW YOUR WORK
6x = 42
8y = 72
-2x = 8
-33x = 66
24x = 72
-x = 26
Solving Two-Step Equations
Rules:
1. To solve a two-step equation,
first undo the addition and
subtraction by performing the
opposite or inverse operation.
2. Then, undo the multiplication
and division by performing the
opposite or inverse operation.
Example:
4x + 5 = 17
4x + 5 – 5 = 17 – 5
4x = 12
4x = 12
4
4
x=3
Check:
3. To check, substitute or
replace the variable with your
solution (answer) to see if it
makes the equation true.
4x + 5 = 17
4(3) + 5 = 17
12 + 5 = 17
17 = 17
Show all your work in your scribbler or binder: Be sure to SHOW YOUR
WORK and SHOW YOUR CHECK!!!
1) 2x + 1 = 7
2) 3n + 1 = 13
3) 4t + 5 = 21
4) 2y + 7 = 11
5) 3p + 2 = 22
6) 4m + 7 = 27
7) 2t + 5 = 15
8) 7c + 2 = 16
9) 2x – 1 = 9
10) 5x – 2 = 13
11) 2x – 5 = 11
12) 4x – 7 = 17
13) 5x – 6 = 24
14) x + 19 = 28
2
18) 2x + 5 = 19
15) 2x – 4 = 11 + 1
16) 6x – 5 = 23 - 4
19) 6p + 14 = 68
20) 12x – 9 = 75
22) 3x – 11 = 10
23) b - 12 = 8
9
27) 5a + 3 = 18
24) 2x + 1 = 7
17) 3y + 6 = 27
21) x + 5 = 10
7
25) a - 2 = 3
4
26) 36 – x = 16
28) 5y – 2.6 = 7.4