Equations Objective solve linear equations with a variable

Equations

Objective: solve linear equations with a variable on one side.

4 a = 24 This means “ 4 multiplied by a” What is the inverse operation? Division a = 24 4 =6

This means “b divided by 5” What is the inverse operation? Multiplication b=3 5 b=3 x 5 = 15

Simple Equations (1 step) n n n Includes variable, one operation, and answer X– 2=8 4+X=8 n 6/x = 3 n 2 x = 10 Kee p th Use e eq INV ERS uati o EO n ba PER lanc ATI O ed! NS to solv e.

Tara and Tom were solving linear equations. To find the value of x in a linear equation, Tara asked herself, “What number, when you subtract four from it, is equal to twelve? ” Tom solved a linear equation by adding four to both sides. It is possible that the two students were solving the same equation? How do you know?

Medium Let’s make this question This is. This the only saysbit into a low thatsimple is “add different. 8” Wequestion. can use We inverse operations What is the know how to to get ridthose! of it. inverse solve Subtract operation? Look! A simple question! 3 a + 8 = 35 3 a = 35 - 8 3 a = 27 3 =9

Equations (2 step) n n n Includes variable, two operations, and answer Kee p th 3 X – 2 = 8 4 + 5 X = 19 6/x + 4 = 7 2 x - 6 = 10 Use e eq uati o INV ERS EO n ba Wor k Ba ckw ards. PER lanc ATI O ed! NS to solv e.

Sal explained how he solved a linear equation by saying, “I undid the addition by subtracting from both sides. Then I undid the multiplication by dividing both sides. That told me the value of x was ten. ” What equation might Sal have solved?

The hand shown is covering a term in a linear equation. What might the hidden term be and what as a result, would be the value of x? 4 + ø= 16

Take it up a level! Objective: solve linear equations with an unknown (variable) both sides.

Level 2 5 a + 3 = 2 a + 12 5 a = 2 a + 12 - 3 Let’s start by 5 a = 2 a + 9 Doing this removes removing this. the add 3, but This says Now, remember let’s remove this. to subtract 5 a – 2 a = 9 add 3 3 from the other side “get 9 rid of” our 2 a, we 3 a. To = What is the too! have to subtract 2 a inverse operation? a = 9 =3 Subtract 3 A 3

Equations (variables on both sides) n n n Includes variable in several places, more than one operation, and answer 7 x + 10 = 2 x 11 x = 24 + 8 x Kee p th Use e eq INV ERS n ba EO Star 8 y – 3 = 6 y +17 t by side gett ! 7 k + 12 = 8 – 9 k uati o ing PER the lanc ATI O vari NS able ed! to s olve on o ne .