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Algebraic Expressions & Equation Solving Guide

Learn how to simplify algebraic expressions, identify like terms, solve linear equations, isolate variables, and apply properties of equality to solve equations effectively. This beginner-friendly guide covers essential concepts with examples.

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Algebraic Expressions & Equation Solving Guide

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  1. Algebraic Expressions

  2. Warm Up Change 0.483 to a Percent Simplify

  3. Like Terms • Term- a number, variable, or product of a number and one or more variables • Ex.: 3a – 4b + 5 has 3 terms • Like Terms- terms with the same variables and the same exponents • Ex.: 2x, 3x 4mn, 12mn • In the term 3a, 3 is called the numerical coefficient Note: and are NOT like terms

  4. Simplify

  5. Simplify

  6. Simplify

  7. Solving Equations

  8. Solving Equations • In this section we are going to learn how to solve linear (or first degree) equations. • A linear equation is one in which the exponent on the variable is 1. • Example: 5x – 1 = 3 2x + 4 = 6x - 5

  9. Equivalent Equations • Equivalent Equations are equations that have the same solution. • The following are equivalent equations: 2x – 5 = 1 2x = 6 x = 3

  10. When we solve an equation, we write the equation as a series of simpler equivalent equations until we obtain an equation of the form x = c, where c is some real number.

  11. Isolate the Variable • To solve any equation, we have to isolate the variable. • That means getting the variable by itself on one side of the equals sign. • There are 4 properties we will use to isolate the variable.

  12. Addition Property of Equality You can add the same number to both sides of an equation and the equation remains equivalent.

  13. Example:

  14. Subtraction Property of Equality You can subtract the same number to both sides of an equation and the equation remains equivalent.

  15. Example:

  16. Multiplication Property of Equality You can multiply the same number on both sides of an equation and the equation remains equivalent.

  17. Example:

  18. Division Property of Equality You can divide the same number on both sides of an equation and the equation remains equivalent.

  19. Example:

  20. Procedure to Solve Equations 1. Get rid of fractions. 2. Distribute when needed. 3. Combine like terms on same side of equals. • Use the addition/subtraction property. You • may have to use it more than once! • Solve using either the multiplication property • or the division property.

  21. Solve

  22. Solve

  23. Solve

  24. Variables on Both Sides • Your goal is to get the variable on one side of the equals sign and everything else on the other side of the equals sign. • Always combine like terms on each side of the equation FIRST!

  25. Example:

  26. Solve

  27. Solve

  28. Grouping Symbols You have to distribute before you combine like terms.

  29. Solve

  30. Solve

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