Objective 3.4 solve equations with variables on both sides.

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Presentation transcript:

Objective 3.4 solve equations with variables on both sides

Equation- mathematical sentence with an equal sign Like a scale, both sides must be EQUAL in order to be balanced.

Solving Equations with Variables on Both Sides How can you get the “unknown” by itself? 7 - 8x = 4x – 17 Solving Equations with Variables on Both Sides STEP 1- Use distributive property and combine like terms. STEP 2- Collect variables on one side of the equation. STEP 3- “Undo” addition and/or subtraction. STEP 4- “Undo” multiplication and/or division. STEP 5- Solve for the variable. STEP 6- Check your work.

Solving Equations with Variables on Both Sides… Isolate the variable! Get ‘x’ by itself. 7 – 8x = 4x – 17. Write original equation. 7 – 8x + 8x = 4x – 17 + 8x Add 8x to each side. 7 = 12x – 17 Simplify each side. 24 = 12x Add 17 to each side. 2 = x Divide each side by 12.

7 – 8x = 4x – 17 x = 2 7 – 8(2) = 4(2) – 17 Are both sides equal? Check Your Work! 7 – 8x = 4x – 17 x = 2 7 – 8(2) = 4(2) – 17 Are both sides equal?

Solving Equations with Variables on Both Sides… Isolate the variable! Get ‘x’ by itself. 9x – 5 = 1 4 (16x + 60). 1 4 (16x + 60). 9x – 5 = Write original equation. 9x – 5 = 4x + 15 Distributive property 5x – 5 = 15 Subtract 4x from each side. 5x = 20 Add 5 to each side. x = 4 Divide each side by 5.

9x – 5 = ¼ (16x + 60) x = 4 9(4) – 5 = ¼ (16(4) + 60) Check Your Work! 9x – 5 = ¼ (16x + 60) x = 4 9(4) – 5 = ¼ (16(4) + 60) Are both sides equal?

Solving Equations with Variables on Both Sides…If Possible Isolate the variable! Get ‘x’ by itself. 2 – 15n = 5(-3n +2) 3x +10 – x = 2(x +5) 2 – 15n = -15n + 10 2x + 10 = 2(x+5) 2 – 15n +15n = -15n +15n + 10 2x + 10 = 2x + 10 2 = 10 Identity No Solution

Guided Practice 2) -17p – 6 = -38 – p 1) 6x + 11 = 2x – 5

Guided Practice 7p + 6 – 3p = -38 + 4p 4 + 2x + 8 = 2(x + 6) 6 ≠ -38 2x + 12 = 2x + 12 No solution Identity All numbers

Geometry Connection Find the area and perimeter of the square. 4x – 2 4x – 2 = 3x + 7 4x – 3x = 7 + 2 3x + 7 x = 9 The perimeter of the square is 34(4) which is 136 units. The area of the square is 34 x 34 which is 1156 square units.

Homework Text p. 150&151 3-31 odds Quiz Friday: Multi-Step Equations