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Multi Step Equations

Explore the process of solving multi-step algebraic equations through detailed examples. This guide illustrates key techniques such as distributing terms, combining like terms, and applying the properties of equality. Learn how to handle equations that lead to no solution or infinitely many solutions. We break down equations step-by-step, ensuring clarity and understanding. Ideal for students looking to enhance their algebra skills, this resource is perfect for mastering the art of solving complex equations.

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Multi Step Equations

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  1. Multi Step Equations

  2. AlgebraExamples 3/8 – 1/4x = 1/2x – 3/4 8(3/8 – 1/4x) = 8(1/2x – 3/4) (Multiply both sides by 8) 8(3/8) – 8(1/4x) = 8(1/2x) – 8(3/4) 3 – 2x = 4x – 6 3 -2x + 2x = 4x + 2x – 6 ( add 2x to both sides) 3 = 6x – 6 3 + 6 = 6x - 6 + 6 ( add 6 to both sides) 9 = 6x ( divide both sides by 6) 3/2 = x `

  3. Examples • Solve: • 5n + 4 = 7(n + 1) – 2n (Distribute) 5n + 4 = 7n + 7 – 2 ( add like terms on same side) 5n + 4 = 5n + 7 ( get like terms on the same side) 5n – 5n + 4 = 5n – 5n + 7 4 = 7 No solution!

  4. Examples • Solve: 7 + 2(x + 1) = 2x + 9 (distribute) 7 + 2x+ 2 = 2x + 9 (add like terms on the same side) 2x + 9 = 2x + 9 ( reflexive property) Infinitely many solutions!

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