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Solve Equations With Variables on Both Sides 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. bkevil Use Steps to Solve Equation: 2(x + 7) + 3 = 5x - 1 2x + 14 + 3 = 5x – 1 2x + 17 = 5x - 1 -5x -5x -3x + 17 = - 1 - 17 - 17 -3x = -18 -3 -3 x= 6 bkevil 1) Get rid of ( ) --distribute 2) Combine like terms 3) Get variables on same side – use inverse operation 4) Solve 2 step equation Undo by using inverse -3 -3 undo 2nd + 17 - 17 undo 1st Check - replace “x” with solution 2(x + 7) + 3 = 5x - 1 2(6 + 7) + 3 =5(6) - 1 2(13) + 3 =5(6) - 1 26 + 3 = 30 - 1 29 = 29 X=6 bkevil 1) Replace X = 6 2) Follow order of operations on both sides of equation 3) Checks is the solution to the equation Use Steps to Solve Equation: -3x + 4 = 5x – 8 -5x -5x -8x + 4 = - 8 -4 -4 -8x = -12 -8 -8 x = 1.5 Get variables on same side of equation – use inverse operation (subtract 5x) Solve 2 step equation Undo by using inverse -8 -8 undo 2nd +4 bkevil -4 undo 1st Use Steps to Solve Equation: 4(1 – 2x) = 4 – 6x 4 – 8x = 4 - 6x +6x + 6x 4 - 2x = 4 -4 -4 -2x = 0 -2 -2 x= 0 Get rid of ( ) -- distribute Get variables on same side – use inverse operation (add 6x) Solve 2 step equation Undo by using inverse -2 -2 undo 2nd +4 bkevil -4 undo 1st Use Steps to Solve Equation: 9 + 5x = 5x + 9 -5x -5x Get variables on same side of equation – use inverse operation (subtract 5x) 9=9 x = any real number The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity The solution is all real numbers bkevil Use Steps to Solve Equation: 6x – 1 = 6x – 8 -6x -6x Get variables on same side of equation – use inverse operation (subtract 6x) -1 = - 8 x = no solutions The solution is no real numbers or empty set bkevil 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. 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. bkevil The end bkevil