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Learn how to solve equations with variables on both sides by following specific steps. Understand how to get rid of parentheses, combine like terms, and isolate the variable to find the solution. Remember two special cases for variable elimination.
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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.
1) Get rid of ( ) --distribute 4) Solve 2 step equation 3) Get variables on same side – use inverse operation 2) Combine like terms 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 Undo by using inverse -3 undo 2nd -3 -3 -3 + 17 -17 undo 1st x = 6
1) Replace X = 6 3) Checks Check - replace “x” with solution2(x + 7) + 3 = 5x - 1 2(6+ 7) + 3 =5(6) - 1 2(13)+ 3 =5(6) - 1 2) Follow order of operations on both sides of equation 26+ 3 =30- 1 29= 29 X = 6 is the solution to the equation
Solve 2 step equation Use Steps to Solve Equation: -3x + 4 = 5x – 8 Get variables on same side of equation – use inverse operation (subtract 5x) -5x -5x -8x + 4 = - 8 - 4 - 4 Undo by using inverse -8x = -12 -8 + 4 -8 undo 2nd -8 -8 -4 undo 1st x = 1.5
Get rid of ( ) -- distribute Solve 2 step equation Use Steps to Solve Equation:4(1 – 2x) = 4 – 6x 4 – 8x = 4 - 6x +6x + 6x Get variables on same side – use inverse operation (add 6x) 4 - 2x = 4 - 4 - 4 -2x = 0 Undo by using inverse -2 -2 -2 + 4 -2 undo 2nd -4 undo 1st x = 0
The solution is all real numbers Use Steps to Solve Equation: 9 + 5x = 5x + 9 Get variables on same side of equation – use inverse operation (subtract 5x) -5x -5x 9 = 9 The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity x = any real number
The solution is no real numbers or empty set Use Steps to Solve Equation: 6x – 1 = 6x – 8 Get variables on same side of equation – use inverse operation (subtract 6x) -6x -6x -1 = - 8 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. x = no solutions
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.