Solving Equations with Variables on Both Sides 4:3

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Presentation transcript:

Solving Equations with Variables on Both Sides 4:3 Write this in your Toolkit. variables and their coefficients Goal: Get all on one side of the equal sign. 2x+6 = 3x+2 -2x AND Move all of the to the opposite side of the equal sign. constants !!!! Important !!! Use addition or subtraction for these steps! +6 = x+2 -2 4 = x

Remember, you move a positive with a negative. You move a negative with a positive.

Put problem in Toolkit: pg. 237 Question: What should you move? x √ 5x = +16 variables and coefficients -1x equivalent equation 4  4 = 16 4x = 16 Divide both sides by 4 to remove the multiplying 4. New, equivalent equation Question: Now, what? Does the answer check? 4x = 16 5x = x +16 4 4 5 4 = 4 + 16 x = 4 20 = 20 √

10 = x 20 + 4x = 6x -4x -4x 20 = 2x New, equivalent equation! 𝟐𝟎 𝟐 = 𝟐𝒙 𝟐 10 = x Check: 20 + 4  10 = 6  10 60 = 60

x = 16 -8 - 8 2x = 32 equivalent equation Pg. 238: Put problems in Toolkit 4x + 8 = 2x + 40 -2x -2x 2x + 8 = 40 equivalent equation -8 - 8 2x = 32 equivalent equation 𝟐𝒙 𝟐 = 𝟑𝟐 𝟐 Divide by coefficient. x = 16 Check: 416 + 8 = 2 16 + 40 64 + 8 = 32 + 40 72=72 √

x = 6 -3x - 3x 6x = 36 equivalent equation Pg. 238: Also, constants can be moved first. 2. 9x - 2 = 34 + 3x +2 +2 9x = 36 + 3x equivalent equation -3x - 3x 6x = 36 equivalent equation 𝟔𝒙 𝟔 = 𝟑𝟔 𝟔 Divide by coefficient. x = 6 Check: 9 6 - 2 = 34 + 3  6 54 - 2 = 34 + 18 52=52 √ Does 6 work in the equivalent equations?

Pg. 238: 6. 11 + 4x = 7 + 5x -7 -7 4 + 4x = 5x equivalent equation -4x - 4x 4 = 1x 4 = x Check: 11 + 4 4 = 7 + 5  4 11 + 16 = 7 + 20 27=27 √ Does 6 work in the equivalent equations? 4 + 4(4) = 5(4) 4 + 16 = 20 20 =20 √

Pg. 238: Choose your method. constant or variable/coefficient 7. 3 - x = 4 - 3x 3 - x = 4 - 3x -3 -3 (Remember, 3 is positive!) +x +1x -x = 1 - 3x Both are equivalent equations. 3 = 4 - 2x +3x +3x - 4 -4 2x = 1 Both are equivalent equations. -1 = -2x 𝟐𝒙 𝟐 = 𝟏 𝟐 ………Divide by coefficient……… −𝟏 −𝟐 = −𝟐𝒙 −𝟐 x = 𝟏 𝟐 𝟏 𝟐 = x Check: 3 - 𝟏 𝟐 = 4 - 3  𝟏 𝟐 2 𝟏 𝟐 = 4 - 𝟑 𝟐 ….. 𝟖 𝟐 - 𝟑 𝟐 = 𝟓 𝟐 = 2 𝟏 𝟐 2 𝟏 𝟐 = 2 𝟏 𝟐 √

Pg. 238: Choose your method. constant or variable/coefficient 9. −x + 4 = −9.8 + x −x + 4 = −9.8 + x -4 -4. Line up decimals. +x +1x -x = -13.8 + x Both are equivalent equations. 4 = −9.8 +2x -x -x Line up decimals. + 9.8 = +9.8 −2x = -13.8 Both are equivalent equations. 13.8 = 2x −𝟐𝒙 −𝟐 = −𝟏𝟑.𝟖 −𝟐 …Divide by coefficient…… −𝟏𝟑.𝟖 −𝟐 = −𝟐𝒙 −𝟐 x = 𝟔.𝟗 𝟔.𝟗 = x 𝟔.𝟗 𝟐 𝟏𝟑.𝟖 Check: -6.9 + 4 = -9.8 + 6.9 +4 +6.9 -2.9 = -2.9 √