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

EquationsEquations

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

4a = 244a = 24This means

“4 multiplied by a”

What is the inverse operation?

Division

a = 24 4

= 6

b = 3b = 355

This means

“b divided by 5”

What is the inverse operation?

Multiplication

b = 3 x 5

= 15

Simple Equations (1 step)Simple Equations (1 step)

Includes variable, one operation, and Includes variable, one operation, and answeranswer

X – 2 = 8X – 2 = 8

4 + X = 84 + X = 8

6/x = 36/x = 3

2x = 102x = 10

Keep the equation balanced!Use INVERSE OPERATIONS to

solve.

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

MediumMedium

3a + 8 = 353a + 8 = 35Let’s make this question into a low simple question. We know how to solve those!

This is the only bit that is different. We can use inverse operations to get rid of it.

This says “add 8”

What is the inverse operation?Subtract

3a = 35 - 83a = 27

Look! A simple question! a = 27

3 = 9

Equations (2 step)Equations (2 step)

Includes variable, two operations, and Includes variable, two operations, and answeranswer

3X – 2 = 83X – 2 = 8

4 + 5X = 194 + 5X = 19

6/x + 4 = 76/x + 4 = 7

2x - 6 = 102x - 6 = 10

Keep the equation balanced!Use INVERSE OPERATIONS to

solve.

Work Backwards.

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

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

4 + 4 + øø= 16= 16

Take it up a level!Take it up a level!

Objective: solve linear equations with Objective: solve linear equations with an unknown (variable) both sides.an unknown (variable) both sides.

Level 2Level 2

5a + 3 = 2a + 125a + 3 = 2a + 12

Let’s start by removing this.

This says add 3What is the inverse operation?

Subtract 3

Doing this removes the add 3, but remember to subtract 3 from the other side too!

5a = 2a + 12 - 35a = 2a + 9

Now, let’s remove this.

To “get rid of” our 2a, we have to subtract 2a

5a – 2a = 93a = 9

a = 9A 3

= 3

Equations (variables on both sides)Equations (variables on both sides)

Includes variable in several places, more Includes variable in several places, more than one operation, and answerthan one operation, and answer

7x + 10 = 2x7x + 10 = 2x

11x = 24 + 8x11x = 24 + 8x

8y – 3 = 6y +178y – 3 = 6y +17

7k + 12 = 8 – 9k7k + 12 = 8 – 9k

Keep the equation balanced!Use INVERSE OPERATIONS to

solve.

Start by getting the variable on

one side!