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Solve Equations With Variables on Both Sides

Solve Equations With Variables on Both Sides. 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

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Solve Equations With Variables on Both Sides

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  1. Solve Equations With Variables on Both Sides

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.

  10. The end

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