Solving Linear Equations MATH 017 Intermediate Algebra S. Rook

2 Overview Section 2.1 in the textbook –General Strategies for Solving Equations –Simplify Before Solving –Equations with the Variable on Both Sides –Equations with Infinite or No Solutions

Solving Equations

4 The objective of an Algebraic equation is to isolate the variable. Think of the equation as a scale – the scale must be balanced at all times. –“What you do to one side, you must do to the other.” Know the difference between equations and expressions –We SOLVE equations (=) –We SIMPLIFY expressions (no =) When in doubt, check your answer back into the equation to see if a true statement results

5 Solving Equations (Example) Ex 1: Solve for x: 3x + 5 = 23

6 Solving Equations (Example) Ex 2: Solve for x: 2x – 7 = 21

Simplify Before Solving

8 Simplify both sides of an equation (if possible) before moving terms across the = –Combine like terms –Apply the Distributive Property –Eliminate fractions

9 Simplify Before Solving (Example) Ex 3: Solve for x: 4x – 5 + 3x – 2 = 10

10 Simplify Before Solving (Example) Ex 4: Solve for x: 2(x – 1) + 3(x – 2) = 12

11 Simplify Before Solving (Example) Ex 5: Solve for x:

Equations with the Variable on Both Sides

13 Equations with the Variable on Both Sides Possible for the variable to exist on both sides of the equation –Must isolate the variable on one side –Usually easier to view when the variable is isolated on the left side of the equation Especially when we deal with inequalities in the next section.

14 Equations with the Variable on Both Sides (Example) Ex 6: Solve for x: 3(x + 3) – 5x = 2x + 9

15 Equations with the Variable on Both Sides (Example) Ex 7: Solve for y:

Equations with Infinite or No Solutions

17 Equations with Infinite or No Solutions Can only happen when the variable drops out on both sides of the equation Determine whether the resulting statement is true or not –If yes, then the equation has an infinite number of solutions and we say the solution is all real numbers. –If no, then the equation has no solution

18 Equations with Infinite or No Solutions (Example) Ex 8: Solve for z: 3(z – 1) = 2z + z – 5

19 Equations with Infinite or No Solutions (Example) Ex 9: Solve for x:

20 Summary After studying these slides, you should know how to do the following: –Understand the rules that must be followed when solving a linear equation –Simplify both sides of an equation before moving terms across the = –Isolate the variable on one side (preferably the left) –Identify when an equation has infinite or no solutions