Integer Equations
Objectives:
…to solve one-step equations involving integers, decimals, and fractions
Assessment Anchor:
Not Available At This Time
NOTES
***EQUATIONS ARE LIKE SEE-SAWS, AND MUST REMAIN BALANCED!!
To solve a one step equation:
1. Locate the variable in the equation
2. Use the inverse (opposite) operation on both sides of the equation
a) We do this to get the variable all by itself
b) You can also think of it as “moving something” to another side
3. Show your answer
EXAMPLES (+ or –)
1)
x – 7 = -22
x – 21 = -30
x – 21 = -30
Add 7 on both sides
x – 7 = -22
+7 +7
x = -15
2)
x + 9 = -13
x + 19 = -8
Subtract 9 on both sides
x + 9 = -13
–9 –9
x = -22
x + 19 = -8
x=
x=
Integer Equations
3)
20 = 34 + x
Subtract 34 on both sides
4)
Add 38 on both sides
20 = 34 + x
– 34 – 34
- 14 = x
-21 = x – 38
-21 = x – 38
+ 38
+ 38
17 = x
8 = 21 + x
8 = 21 + x
=x
-11 = x – 31
-11 = x – 31
=x
MORE EXAMPLES(+ or –)
y + 28 = -8
k – 19 = -7
3 = 11 + z
h + 20 = -31
-13 = x – 32
g – 17 = -29
-16 = x – 18
b + 14 = -14
k – 29 = -8
x + 21 = 13
-24 = -11 + x
z + 33 = 16
Integer Equations
EXAMPLES (× or ÷)
1)
-20 = 2x
Divide by 2 on both sides
-20 = 2x
2 2
-10 = x
2)
4x = -72
4x = -72
x=
9=x
-7
x = -11
-3
Multiply by -7 on both sides
-7 • 9 = x • -7
-7
-63 = x
x = -11
-3
x=
3)
-5y = -30
-3x = -36
Divide by 2 on both sides
-5y = -30
-5
-5
y=6
4)
x = -8
-9
-9 • x = -8 • -9
-9
x = 72
Multiply by -7 on both sides
-3x = -36
x=
x = -19
5
x = -19
5
x=
MORE EXAMPLES (× or ÷)
-4x = -48
x=8
-6
k = -12
5
Integer Equations
36 = -4k
-40 = 8y
b = -15
2
-8m = -200
h = -5
-11
6=z
-10
EXAMPLES (with decimals)
-4x = -2.28
k + 2.35 = -1.9
-5.8 = x – 3.7
m = -4.8
3
-40.1 + y = -13
9.18 = y + 10.8
3.57 = 6.2 + x
-0.05h = 0.38
2.4 = x
-1.1
Integer Equations
EXAMPLES (with fractions)
***If there is a fraction being multiplied by a variable, you can get rid of it by
MULTIPLYING ON BOTH SIDES BY THE RECIPROCAL!!
⅓ m = -8
½ x = -3
-¼ y = -10
-5 = -½ x
15 = -¾ p
-⅔ g = -10
⅞ h = -7
-⅜ x = -6
-3 = ⅝ b