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bkevil Solve Equations With Variables on Both Sides

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bkevil Steps to Solve Equations with Variables on Both Sides 1) Get rid of ( ) on both sides of equation. 2) Combine like terms on both sides. 3) Get variable on one side of the equation 4) Solve 2 step equation by undoing what has been done to the variable.

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bkevil Use Steps to Solve Equation: 2(x + 7) + 3 = 5x - 1 2x + 14 + 3 = 5x – 1 1) Get rid of ( ) --distribute 2) Combine like terms 2x + 17 = 5x - 1 -5x 3) Get variables on same side – use inverse operation -3x + 17 = - 1 4) Solve 2 step equation -3 + 17 Undo by using inverse -3 undo 2 nd - 17 undo 1 st - 17 - 17 -3x = -18 -3 -3 x = 6

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bkevil Check - replace “x” with solution 2(x + 7) + 3 = 5x - 1 1) Replace X = 6 2(6 + 7) + 3 =5(6) - 1 2) Follow order of operations on both sides of equation 2(13) + 3 =5(6) - 1 26 + 3 = 30 - 1 29 = 29 3) Checks X = 6 is the solution to the equation

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bkevil Use Steps to Solve Equation: -3x + 4 = 5x – 8 -5x Get variables on same side of equation – use inverse operation (subtract 5x) -8x + 4 = - 8 Solve 2 step equation -8 + 4 Undo by using inverse -8 undo 2 nd - 4 undo 1 st - 4 - 4 -8x = -12 -8 -8 x = 1.5

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bkevil Use Steps to Solve Equation: 4(1 – 2x) = 4 – 6x 4 – 8x = 4 - 6x Get rid of ( ) -- distribute Get variables on same side – use inverse operation (add 6x) 4 - 2x = 4 Solve 2 step equation -2 + 4 Undo by using inverse -2 undo 2 nd - 4 undo 1 st - 4 - 4 -2x = 0 -2 -2 x = 0 +6x + 6x

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bkevil Use Steps to Solve Equation: 9 + 5x = 5x + 9 -5x -5x Get variables on same side of equation – use inverse operation (subtract 5x) The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity 9 = 9 x = any real number The solution is all real numbers

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bkevil Use Steps to Solve Equation: 6x – 1 = 6x – 8 -6x Get variables on same side of equation – use inverse operation (subtract 6x) The variables zeroed out and remaining is a false statement where a number is equal to a different number, so there will be no number that will work in the equation. -1 = - 8 x = no solutions The solution is no real numbers or empty set

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bkevil Review Steps to Solve Equations with Variables on Both Sides 1) Get rid of ( ) on both sides of equation. 2) Combine like terms on both sides. 3) Get variable on one side of the equation. 4) Solve 2 step equation by undoing what has been done to the variable. 5) Remember 2 special cases when the variable zeros out.

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bkevil The end

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