Download 2.7 Solving equations involving integers A number may be ,

2.7 Solving equations involving integers
A number may be +,-,⋅, ÷ to each side of an equation to get an equivalent equation
Solve the equations
Check
Examples:
Solve:
Example1
− 4 + x = −12
+4
+4
x = −8
Check:−4 + x = −12
−4 + −8
= −12
−12
Therefore x = −8
is a solution
Example 3
−3 + 7 = h + 11−2
Simplify both sides of the equation first
4 = h + −22
+22
+22
26 = h
Check:−3 + 7 = h + 11−2
−3 + 7 = 26 + 11−2
Simplify
4 = 26 − 22
Therefore h = 26
is a solution
4=4
Example 4
Solve: a. −3x = 15 and b. −16 = −4y
a. −3x = 15 Divide each side by -3
÷−3  ÷−3 
1x = −5, x = −5
Check: −3x = 15
−3−5 = 15
15 = 15 so x = −5 is a solution
b. −16 = −4y
Divide each side by -4
÷ −4 ÷ −4
4 = 1y , 4 = y or y = 4
Check: −16 = −4y
− 16 = −44
−16 = −16 so 4 = y is a solution
Example 5
Solve: −5x = −10 Multiply each side by -5
1
−5 −5x = −10−5
1x = 50, or x = 50
x
Check: −5 = −10
50
= −10
−5
−10 = −10 so x = 10 is a solution
Example 6 Solutions involving -x
Solve: −x = 9 Use meaning of -x
−1x = 9 Multiply each side by -1
−1−1x = 9−1
1x = −9, or x = −9
Check:−x = 9
−−9 = 9
9 = 9 so x = −9 is a solution
__________________________________
Solve: −x = −9
−1x = −9
−1−1x = −9−1
x=9
Do NOW
Solve the equations:
1. − 6 + y = −8
2. −2 + 8 = y + 3−4
3. −40 = −8f,
4. −3t = 4,
5.−h = −10
Check
Ans: -2,18,5,-12,10
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Combine operations
#46. −10 + −2 = −4x
−12 = −4x
−12
= −4x
=4
−4
3 = x or x = 3
Check:−10 + −2 = −4x
− 10 + −2 = −43
−12 = −12 so x = 3
# 53
x
−2
is a solution
= −6 + 3
2
= −3
−2 −2x = −3−2
x=6
6
= −6 + 3
Check: −2
6
= −6 + 3
−2
−3 = − −3 so x = 6
# 58 5y + 1 = −9
5y + 1 − 1 = −9 − 1
5y = −10
5y
= −10
5
5
y = −2
Check: 5−2_ + 1 = −9
−10 + 1 = −9
−9 = −9 so y = −2
x
−2
#66 12 = −9 − 3x
12 + 9 = −9 + 9 − 3x
21 = −3x
21
= −3
x
−3
−3
−7 = x or x = −7
Check: 12 = −9 − 3x
12 = −9 − 3−7
12 = −9 + 21
12 = 12 so x = 7
is a solution
is a solution
is a solution
# 70 −7 − 5 − 7x = 16
−12 − 7x = 16
−12 + 12 − 7x = 16 + 12
− 7x = 28
−7x
28
= =7
−7
x = −4
Check: −7 − 5 − 7x = 16
− 7 − 5 − 7−4 = 16
− 12 + 28 = 16
16 = 16 so x = −4
is a solution
g
# 80 −5 = 4 + −4
g
−5 − 4 = 4 − 4 + −4
g
−9 = −4
g
−9−4 = −4 −4
36 = g or g = 36
#86 −y = 12
3
−1y = 12
−1y
12
= =1
−1
y = −12
Do NOW −6b − 1 = 11, 6 − 8k = −34,
r − −7 = −1 − 6
8 = −3x + 2,
m
−8
− 10 = −27,
ans. -2,5,32,-2,-14
Word Problems: p141
#91 1st year down 43 pts (points)
5th year down only 9 pts
How many points were picked up?
___________________________________
1st year + pickup = 5th year
-43 + p
= -9
# 93 Deposit $220
Balance: overdrawn $215 (-$215)
What was balance before deposit?
___________________________________
Old Balance + deposit = new balance
o
+ 220 = -215
#97Price dropped each month
At years end drop was $60
What was the drop each month (drop/month)
___________________________________
yearly drop ( 1yr/12mo) = drop/month
60 (1/12) = m
4