# Solving Equations with Variables on Both Sides Using the Equation Ladder

In this lesson, you will learn how to solve equations with variables on both sides by following the Equation Ladder. You will simplify both sides of the

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## About Solving Equations with Variables on Both Sides Using the Equation Ladder

PowerPoint presentation about 'Solving Equations with Variables on Both Sides Using the Equation Ladder'. This presentation describes the topic on In this lesson, you will learn how to solve equations with variables on both sides by following the Equation Ladder. You will simplify both sides of the. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

Slide1MCC8.EE.7 a and b:  Solving Equations with Variables on Both Sides. • Follow the  Equation Ladder . • Simplify both sides of the equation using the distributive property and/or combining like terms. •  Add/subtract to get rid of the variables on one side of the equation (think positive). • Add/subtract to get constants alone on the other side. • Multiply/divide so the variable has a coefficient of 1.

Slide2Equations w/ Variables on Both SidesLinear equations can have -   exactly one solution .  (We’ve seen this) -  no solution .  (We haven’t seen this.) -  infinitely many solutions .  (Or this.) No solution   and  infinitely many solutions occur when the variable “ falls out ” of the equation you are trying to solve.

Slide3Equations w/ Variables on Both SidesIf the equation has  no solution ,  when the variable falls out, the statement left behind is obviously false , like 4 = 7. Say, “no solution.” If the equation has  infinitely many solutions , when the variable falls out, the statement left behind is  obviously true , (your book calls this an identity) like 5 = 5 or 0 = 0. Say, “infinitely many solutions” or just “many solutions.”

Slide4Equations w/ Variables on Both SidesExample: 6(x + 4) = 4x + 2x – 12 6x + 24 = 6x – 12 –6x –6x 24 – 12 = Obviously false, so equation  has no solution. < --Distribute on the left, combine like terms on the right. <-- Subtract 6x on each side.

Slide5Equations w/ Variables on Both SidesExample: 3(x + 4) = 4 + 3x + 8 3x + 12 = 3x + 12 –3x –3x 12 12 = Obviously true, so this equation  has infinitely many solution. < --Distribute on the left, combine like terms on the right. <-- Subtract 3x on each side.