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OPENER: Solve and CHECK the following equations. 1.) − 12 + a = − 362.) t – ( − 16) = 9 3.)...
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OPENER : Solve and CHECK the following equations. 1.) −12 + a = − 36 2.) t – (−16) = 9 10 5 2 y 3.) ¼ + x = ⅔ 4.) +12 +12 t + 16 = 9 a = -24 -16 -16 t = -7 -¼ -¼ x = 12 5 12 3 12 8 2 5 ) 1 10 ( ) 5 2 ( 2 5 y y = 25
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Solve Multi-Step Equations To solve equations with more than one operation, often called multi-step equations, undo operations by working backwards. For example, 2x + 1 = x = x = 4 CHECK!! 2x + 1 = 9 2(4) + 1 = = 9 9 = 9
Transcript of OPENER: Solve and CHECK the following equations. 1.) − 12 + a = − 362.) t – ( − 16) = 9 3.)...
OPENER: Solve and CHECK the following equations.1.) −12 + a = − 36 2.) t – (−16) =
9
1052
y3.) ¼ + x = ⅔ 4.)
+12 +12 t + 16 = 9
a = -24 -16 -16
t = -7
-¼ -¼
x = 125
123
128
25)
110()
52(
25
y
y = 25
Algebra 1 ~ Chapter 3 - 4
Solving Multi-Step Equations
Solve Multi-Step Equations To solve equations with more than one operation, often called multi-step equations, undo operations by working backwards.
For example, 2x + 1 = 9 -1 -1 2x = 8 2 2
x = 4
CHECK!!
2x + 1 = 9
2(4) + 1 = 9
8 + 1 = 9
9 = 9
Example – Solve and Check!1.) 7m – 17 = 60 + 17 +17
7m = 77 7 7
m = 11
CHECK
7m – 17 = 60
7(11) – 17 = 60
77 – 17 = 60
60 = 60
2.) − 2a + 10 = 22 - 10 -10
-2a = 12 -2 -2
a = -6
CHECK-2a + 10 = 22-2(-6) + 10 = 2212 + 10 = 2222 = 22
Example – Solve and Check each equation.3.)
-6 -6
y = -153
4563
y
513
y
3)51()3(3 y
4.)
4x + 5 = -35
- 5 -5
4x = -40
4 4
x = -10
5754
x
7)5()754(7
x
Examples – Solve and Check!!5.) 6.)
118
23
a 1724
b
Writing EquationsEx. 1 – “Twelve decreased by twice a number equals -34.”
12 – 2n = -34
Ex. 2 - “Two-thirds of a number minus six is -10.”
⅔n – 6 = -10
Ex. 3 – “A number is multiplied by seven, and then the product is added to 13. The result is 55.”
7n + 13 = 55
Solve a Consecutive Integer Problem*** Find three consecutive integers whose sum is 42.
“3 #’s in a row”
Integer #1 = n
Integer #2 = n + 1
Integer #3 = n + 2 (n) + (n + 1) + (n + 2) = 42
3n + 3 = 42
3n = 39
n = 13
Conclusion - The three consecutive integers whose sum is 42 are 13, 14 and 15.
*** 13 + 14 + 15 = 42
Example – Find three consecutive ODD integers whose sum is -51.Integer #1 = n
Integer #2 = n + 2
Integer #3 = n + 4
Remember we are only looking for odd numbers, so every OTHER number!!
(n) + (n + 2) + (n + 4) = -51
3n + 6 = -51
3n = -57
n = -19
So the three consecutive odd integers are -19, -17 and -15.
Example – Find three consecutive EVEN integers whose sum is 72.Integer #1 = n
Integer #2 = n + 2
Integer #3 = n + 4
Remember we are only looking for even numbers, so every OTHER number!!
(n) + (n + 2) + (n + 4) = 72
3n + 6 = 72
3n = 66
n = 22
So the three consecutive even integers are 22, 24 and 26.
