Download Example 1

1.1 Solving Simple Equations
Learn from other people’s mistakes, because you can’t make
ALL the mistakes yourself!
Becky Wilkes
An equation is a statement formed by placing an equal sign between two
expressions. An equation has a left side and a right side.
4x + 1 = 9
When the variable in an equation is replaced by a number, the resulting
statement is either true or false. If the statement is true, the number is a
solution of the equation.
Define solution.
The value or values of the variable that make
the statement true.
Check if x = 3 is or is not a solution of the equation 5x – 7 = 8.
Write the problem.
Substitute.
Simplify.
Conclusion.
5x – 7 = 8
5(3) – 7 = 8
15 – 7 = 8
8=8
solution
Remember: In
algebra work
downward.
Highlight or
circle your
answer. Skip
one line after
the answer.
Example 1 Check if x = 4 is or is not a solution of the equation 5x – 7 =
8.
5x – 7 = 8
5(4) – 7 = 8
20 – 7 = 8
13
8
not a solution
Are your equal signs in alignment?
Use mental math to solve the equation. Then check the solution.
Write the problem.
Solve mentally.
Check.
7h = 28
h=4
7(4) = 28
28 = 28
Example 2 Use mental math to solve the equation. Then check the
solution.
9 = 17 – x
x=8
9 = 17 – (8)
9=9
Note: Remember to use parentheses when substituting.
Example 3 Use mental math to solve the equation. Then check the
solution.
11 + y = 16
y=5
11 + (5) = 16
16 = 16
Two operations that undo each other, such as addition and subtraction, are called
inverse operations. Inverse operations help you to isolate the variable on one
side of the equal sign.
The problem.
Use inverse property.
Simplify.
Check
x - 7 = -6
+7 +7
x =1
x - 7 = -6
(1) - 7= -6
-6 = -6
y + 3.4 = 0.5
-3.4 -3.4
x = -2.9
y + 3.4 = 0.5
( -2.9) + 3.4 = 0.5
0.5 = 0.5
Example 1 Solve.
1. Write the problem.
2. Undo addition.
Check
27  m  50
 27
3. Simplify.
Remember: In
algebra work
downward. Line up the
equal signs. Skip one
line after the answer.
 27
m  23
27  m  50
27  23  50
50 
 50
Example 2 Solve.
1. Write the problem.
2. Undo subtraction.
3. Simplify.
Check
c  23   40
 23
 23
c  17
c  23   40
 17   23   40
 17    23   40

 40   40
Remember: In
algebra work
downward. Line up
the equal signs.
Skip one line after
the answer.
Example 3 Solve.
1. Write the problem.
2. Undo double sign.
3. Undo subtraction.
4. Simplify.
Check
 40  n   19   40  n   19 
 40  n  19
 40   21   19 

 19  19
 40  40
 21  n
Check your form.
Are the equal signs
in alignment?
Example 4 Solve.
Check
2. Undo double sign.
 11  n   2
 11  n  2
3. Undo addition.
+––
4. Simplify.
 13  n
1. Write the problem.
To avoid sign
errors,
change
subtraction to
addition!
2
2
Check your form.
Are the equal
signs in
alignment?
 11  n   2
 11   13   2
 11  13  2

 11  11
Example 5 Solve.
1. Write the problem.
2. Simplify both sides.
3. Undo subtraction.
4. Simplify.
 7 5   m  30  49
 35  m   19 
 35  m  19
 19
 19
 16  m
Multiplication and division are inverse operations. You can use multiplication
to undo division, and division to undo multiplication.
The problem.
Use inverse property.
Simplify.
1
3x  15
3
3
x  5
Check
3x  15
3 5  15

 15  15
y
4 4  94 
y  36
1
Check
y
9
4
36
9
4
9
9
Example 1 Solve.
1. Write the problem.
2. Use inverse property.
3. Simplify.
Check
1
 3x  2
3 3
2
x
3
 3x  2
2
 3    2
 3 
22
Use good form - place the negative sign out front in your answer.
Example 2 Solve.
1. Write the problem.
2. Use inverse property.
3. Simplify.
Check
1
 4x   22
4
4
22
x
4
11
x
2
 4x  22
2
11
 4/   22
 2/
 211  22

 22  22
Leave the fraction improper – however it must be in lowest terms.
Check
Example 3 Solve.
1
1. Write the problem.
2. Use inverse property.
3. Simplify.
Do
your arithmetic
 25
off to
calculations
9
the side (margins).
9  m  25 9 
m
 25
9
9
m  225
 225
9
 25

 25  25
Check
Example 4 Solve.
1. Write the problem.
2. Use inverse property.
3. Simplify.
Do
your arithmetic
 54

off to
calculations
6
the side (margins).
1
d  6 
 6  54 
6
324  d
d
 54 
6

324
 54 
6

 54  54
Check
Example 5 Solve.
1. Write the problem.
2. Use inverse property.
1
1
7  8
  8 14   /

/

y
 /
 /
 /

7
7
8
/




 16  y
2
3. Simplify.
To solve an equation with
a fractional coefficient,
multiply each side of the
equation by the
reciprocal of the
fraction.
7
14   y
8
7 /
14    16 
8/
–2

14  14
Example 7 Write an equation for: The product of negative twelve and a
number is negative seventy-two. Then solve the equation.
1
1. Translate.
2. Solve.
 12n   72
 12  12
n6
Check
 12n  72
 126  72

 72  72
A discounted concert ticket costs $18 less than the original price
p. You paid $64 for the discounted ticket. Write and solve an
equation for the original price of the ticket.
p -18 = 64
+18 +18
p = 82
The original price of the ticket was $82.