BELL WORK

Solve the following equations for x.

5x = 45

4x + 5 = 13

x = 9

x = 2

HANDS ON EQUATIONS

EACH TABLE HAS…

Two Hands On Equations laminated scale sheets in the learning goals folder.

Two sets of pawns and number cubes and the pencil box.

IMPORTANT VOCABULARY

Coefficient - A number by which a variable is multiplied.

Constant - A term in an expression that does not change in value because it does not

contain a variable.

Like Terms – Terms whose variables are the same.

Variable – A symbol for a number we don’t know yet. This is usually represented by a

letter like x or y.

HOW IT WORKS

We will use our practice sheets to solve the given linear equations. The pawns are our variables and the cubes are our

constants.

Think of the middle of the scale as the equal sign.

Whatever we do on one side of our scale, we must do the same thing on the other side. These are legal moves.

Always go back to check your answer and make sure it balances your scale.

KEEP YOUR SCALE BALANCED. WHATEVER IS DONE TO ONE SIDE MUST BE DONE TO

THE OTHER SIDE.

PRACTICE SHEET #1

Let’s try one together.

Place two blue pawns on the left side of your scale.

Place the number cube on 10 on the right side of your scale.

Two blue pawns equal 10. What number, when multiplied by 2, equals 10.

x = 5Go back and check your work. Plug in 5 for each pawn.

2 (5) = 10 10 = 10

PRACTICE SHEET #1

x = 7Go back and check your work. Plug in 7 for each pawn.

7 + 2 = 9 9 = 9

Let’s try #2 on your worksheet. This problem has an additional step. Remember to keep your scales balanced and only do legal moves.

FIRST STEP: Combine like terms on one side of the equal sign.

Take 2 away from each side.

PRACTICE SHEET #1

x = 2Go back and check your work. Plug in 2 for each pawn.

2 (2) + 3 = 7 4 + 3 = 7 7 = 7

Remember to keep your scales balanced and only do legal moves.

FIRST STEP: Combine like terms on one side of the equal sign.

First Step: Take 3 away from each side.2x = 4

What times 2 equals 4?

PRACTICE SHEET #1

x = 4Go back and check your work. Plug in 4 for each pawn.

4 + 8 = 3 (4) 12 = 12

Remember to keep your scales balanced and only do legal moves.

FIRST STEP: Combine like terms on one side of the equal sign.

First Step: Take 1 pawn away from each side.8 = 2x

What times 2 equals 8?

PRACTICE SHEET #1

x = 1Go back and check your work. Plug in 1 for each pawn.

2(1) + 2 = 4 4 = 4

Remember to keep your scales balanced and only do legal moves.

Take 2 away from each side.2x = 2

What times 2 equals 2?

PRACTICE SHEET #1

x = 6Go back and check your work. Plug in 6 for each pawn.

6 + 8 = 10 + 414 = 14

Keep your scales balanced and only do legal moves.

Remember to combine like terms.

x + 8 = 14Take 8 away from each side.

PRACTICE SHEET #1

x = 4Go back and check your work. Plug in 4 for each pawn.

2(4) = 4 + 48 = 8

Keep your scales balanced and only do legal moves.

Remember to combine like terms.

Take 1 pawn away from each side.

PRACTICE SHEET #1

x = 4Go back and check your work. Plug in 4 for each pawn.

3(4) + 2 = 7 + 712 + 2 = 14

14 = 14

Keep your scales balanced and only do legal moves.

FIRST STEP: Remember to combine like terms.

Take 2 away from each side.3x = 12

Divide both sides by 3 to find the value of x.

PRACTICE SHEET #1

You try #9 and 10 on your own.Remember to check your answer!!

PRACTICE SHEET #2

x = 3Go back and check your work. Plug in 3 for each x.

2(3) = 3 + 36 = 6

Keep your scales balanced and only do legal moves.

Get everything with a variable on one side of the equal sign and everything without a variable on the other side of the equal sign.

Take 1 x away from each side.

PRACTICE SHEET #2

x = 2Go back and check your work. Plug in 3 for each x.

3(2) = 2 + 46 = 6

Keep your scales balanced and only do legal moves.

Get everything with a variable on one side of the equal sign and everything without a variable on the other side of the equal sign.

Take 1 x away from each side.2x = 4

Divide both sides by 2 to solve for x.

PRACTICE SHEET #2

x = 1Go back and check your work. Plug in 1 for each x.

1 + 4 = 2(1) + 35 = 5

Keep your scales balanced and only do legal moves.

Get everything with a variable on one side of the equal sign and everything without a variable on the other side of the equal sign.

Take 1 x away from each side.4 = x + 3

Take 3 away from each side.

PRACTICE SHEET #2

x = 3Go back and check your work. Plug in 3 for each x.

4(3) = 2(3) + 6 12 = 6 + 6

12 = 12

Keep your scales balanced and only do legal moves.

Get everything with a variable on one side of the equal sign and everything without a variable on the other side of the equal sign.

Take 2x away from each side.2x = 6

Divide each side by 2.

PRACTICE SHEET #2

x = 4Go back and check your work. Plug in 4 for each x.

3(4) = 12 12 = 12

Keep your scales balanced and only do legal moves.

Combine like terms on each side of the equal sign.

3x = 12Divide each side by 3.

PRACTICE SHEET #2

x = 7Go back and check your work. Plug in 7 for each x.

2(7) + 1 = 10 + 514 + 1 = 15 15 = 15

Keep your scales balanced and only do legal moves.

Get everything with a variable on one side of the equal sign and everything without a variable on the other side of the equal sign.

Take 1 away from each side.2x = 14

Divide both sides by 2.

PRACTICE SHEET #2

x = 8

Go back and check your work. Plug in 8 for each x. 8 + 8 = 10 + 6

16 = 16

Keep your scales balanced and only do legal moves.

Take 8 away from each side.

PRACTICE SHEET #2

x = 4Go back and check your work. Plug in 4 for each x.

2(4) + 5 = 3(4) + 1 8 + 5 = 12 + 1

13 = 13

Combine like terms. Get everything with a variable on one side of the equal sign and everything without a variable on the other

side.

Take 2 pawns away from each side.5 = x + 1 - Are we done yet?

No, we still have to take 1 away from each side.

PRACTICE SHEET #2

You try #9 and 10 on your own.REMEMBER TO CHECK YOUR ANSWER.