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Mastering One-Step and Multi-Step Equations: A Comprehensive Guide

This detailed guide by Savana Bixler explains the processes of solving one-step and multi-step equations, covering various operations including subtraction, addition, division, and multiplication. It provides clear examples for both single-variable and multi-variable equations, illustrating the steps needed to find the solution. Each method is broken down to ensure understanding, emphasizing the use of inverse operations. Whether you’re just starting with algebra or need a refresher, this resource is perfect for mastering essential skills in solving equations.

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Mastering One-Step and Multi-Step Equations: A Comprehensive Guide

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  1. By: Savana Bixler Solving Equations

  2. One step(subtraction) Subtraction: 1) x+5=20 -5=-5 x=15 • Subtract 5 from both sides

  3. One step(addition) addition Z-25=12 +25=+25 Z=37 • Add 25 to both sides

  4. One step(division) Division: 3x=6 3=3 X=2 • Divide by 3 on both sides

  5. One step(multiplication) Multiplication: *6 (x/6)=5 *6 X=30 • Multiply 6

  6. Two step(addition, division) Addition and division: 3x-2=7 +2=+2 3x=9 3=3 X=3 • Add 2 to both sides. • Divide by 3 on both sides.

  7. Two step(subtraction, division) Subtraction and division: 3x+2=14 -2=-2 3x=12 3=3 X=4 • Subtract 2 from both sides • Divide by 3 on both sides

  8. Two step(addition, multiplication) Addition and multiplication: z/2-6=8 +6=+6 *2 z/2=14 *2 Z=28 • Add 6 to both sides • Multiply 2 on both sides

  9. Two step(addition, multiplication) Addition and multiplication: z/4-2=6 +2=+2 *4 z/4=8 *4 Z=32 • Add 2 to both sides • Multiply 4 on both sides

  10. Multi-step equation(two variables-same sides) Same sides: 2x+5x=49 7x=49 • 7 X=7 • Combine like terms • Divide by 7 on both sides

  11. Multi-step equation(two variables-different sides) Different sides: 7x-5=4x+8 -4x -4x 3x=13 3=3 X=4.333 • Get your variables on the same sides by subtracting 2x from both sides • Add 5 to both sides • Divide both sides by 3

  12. Multi-step equations(using distributive property) Distributive property: 3(x+4)=9 3x+12=9 -12=-12 3x=-3 3=3 X=-1 • Distribute the 2 from the out side of the parenthesis • Subtract 6 from both sides • Divide both sides by 3

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