Solve the following equations for x. 5x = 45 4x + 5 = 13 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.

Go back and check your work. Plug in 5 for each pawn. 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 = 5 Go back and check your work. Plug in 5 for each pawn. 2 (5) = 10 10 = 10

PRACTICE SHEET #1 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. x = 7 Go back and check your work. Plug in 7 for each pawn. 7 + 2 = 9 9 = 9

PRACTICE SHEET #1 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? x = 2 Go back and check your work. Plug in 2 for each pawn. 2 (2) + 3 = 7 4 + 3 = 7 7 = 7

PRACTICE SHEET #1 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? x = 4 Go back and check your work. Plug in 4 for each pawn. 4 + 8 = 3 (4) 12 = 12

PRACTICE SHEET #1 Remember to keep your scales balanced and only do legal moves. Take 2 away from each side. 2x = 2 What times 2 equals 2? x = 1 Go back and check your work. Plug in 1 for each pawn. 2(1) + 2 = 4 4 = 4

PRACTICE SHEET #1 Keep your scales balanced and only do legal moves. Remember to combine like terms. x + 8 = 14 Take 8 away from each side. x = 6 Go back and check your work. Plug in 6 for each pawn. 6 + 8 = 10 + 4 14 = 14

PRACTICE SHEET #1 Keep your scales balanced and only do legal moves. Remember to combine like terms. Take 1 pawn away from each side. x = 4 Go back and check your work. Plug in 4 for each pawn. 2(4) = 4 + 4 8 = 8

PRACTICE SHEET #1 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. x = 4 Go back and check your work. Plug in 4 for each pawn. 3(4) + 2 = 7 + 7 12 + 2 = 14 14 = 14

Remember to check your answer!! PRACTICE SHEET #1 You try #9 and 10 on your own. Remember to check your answer!!

PRACTICE SHEET #2 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. x = 3 Go back and check your work. Plug in 3 for each x. 2(3) = 3 + 3 6 = 6

PRACTICE SHEET #2 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. x = 2 Go back and check your work. Plug in 3 for each x. 3(2) = 2 + 4 6 = 6

PRACTICE SHEET #2 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. x = 1 Go back and check your work. Plug in 1 for each x. 1 + 4 = 2(1) + 3 5 = 5

PRACTICE SHEET #2 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. x = 3 Go back and check your work. Plug in 3 for each x. 4(3) = 2(3) + 6 12 = 6 + 6 12 = 12

PRACTICE SHEET #2 Keep your scales balanced and only do legal moves. Combine like terms on each side of the equal sign. 3x = 12 Divide each side by 3. x = 4 Go back and check your work. Plug in 4 for each x. 3(4) = 12 12 = 12

PRACTICE SHEET #2 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. x = 7 Go back and check your work. Plug in 7 for each x. 2(7) + 1 = 10 + 5 14 + 1 = 15 15 = 15

PRACTICE SHEET #2 Keep your scales balanced and only do legal moves. Take 8 away from each side. x = 8 Go back and check your work. Plug in 8 for each x. 8 + 8 = 10 + 6 16 = 16

PRACTICE SHEET #2 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. x = 4 Go back and check your work. Plug in 4 for each x. 2(4) + 5 = 3(4) + 1 8 + 5 = 12 + 1 13 = 13

REMEMBER TO CHECK YOUR ANSWER. PRACTICE SHEET #2 You try #9 and 10 on your own. REMEMBER TO CHECK YOUR ANSWER.