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# Solving Linear Equations

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1. Solving Linear Equations By: Mary Lazo

2. Various Ways to Solve Linear Equations • Linear equations can be solved: • Algebraically • Graphically • Method 1- graph one equation and identify x-intercept. • Method 2- graph two equations and identify the intersection.

3. Note: • To solve algebraically you must be able to combine like terms and use correct order of operations forward and backward. • Combining like terms- a term is each single part of an expression. Terms combined with the same constants or variables. • Order of operations- PEMDAS; Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

4. Solving Linear Equations Algebraically • Goal: get the variable you are solving for on one side of the equation all by itself. • You can do so by: • Distributive property • Associative property • commutative property • inverse operations. Ex: 3(x+5)-(x+2)-12=7 3x+15-x-2-12=7 2x+1=7 2x=6 x=3 *you can also check your answer by substituting it for “x” into the original equation.

5. Solving Linear Equations Graphically • Method 1– rearrange the equation so that everything is on one side equal to zero. Ex: 14x=12(x+3) Step 1: subtract 14x from both sides, distribute the 12, and combine the “x” terms. Step 2: graph the linear equation y = -2x+36 Step 3: identify the x-intercept of the linear graph, which is x=18 Step 4: check your answer by substituting 18 for “x” in the original equation.

6. Solving Linear Equations Graphically • Method 2-set each side of the equation equal to “y” to get two separate linear functions. When you graph both functions on the same graph and find their intersection point, you have found the answer to the problem. Ex: 3(x+5)=21 Step 1: set up 2 linear funtions y=3x+15; y=21 Step 2: graph both functions to find intersection at (2,21), therefore the solution is x=2. Step 3: check your answer by substituting 2 in for “x” in original equation.

7. Setting up Linear Equations to be Solved • To correctly set up a linear equation, you must know the translations of key terms. • “is” means = • “sum” or “total” mean + • “difference” or “less than” mean – Ex: The difference between three times a number and four is five times the number. Step 1: translate sentence The difference between(subtract) three times a number(3n) and four(4) is(=) five times the number(5n). Step 2: write the sentence using symbols instead of words. “subtract 3n and 4” means 3n-4, therefore, 3n-4=5n.

8. Solve a Real World Linear Equation • Ex: Tory is taking a typing class. When he began he typed the practice paper in a rate of 15 words per minute. After 3 months practice, he can type the same practice paper at a rate of 65 words per minute which saves him 8 minutes of typing time. Write an equation that can be used to find the time it took Tory to type the paper on the first day and then solve to find out how long it takes him to type the same paper today. Step 1: Translate the sentence Step 2: Write the sentence using symbols instead of words. Step 3: Solve the equation Step 4: Translate the meaning of the solution Solution: It takes Tory 2 minutes and 24 seconds to type the practice paper today.

9. Refrences/Credits • Wilcox, T. (2009). Combining Like Terms. Retrieved October 2009, from Free Math Help: http://www.freemathhelp.com/ combining-like-terms.html • Services, T. P. (2003-2005). Solving Linear Equations. Retrieved October 2009, from TexasMath.com: http://www. texasmath.com/jsp/lessons/Obj4/One/four_1.html