I’m thinking of a number between 1 and 10…. Can you guess my number? play again

Solving One Step Equations

Solve one-step equations in one variable by using addition,subtraction multiplication, or division. Objective equation solution of an equation Vocabulary

An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, isolate the variable. That means it is on one side of the “=“ and everything else is on the other side.

Inverse Operations OperationInverse Operation AdditionSubtraction Addition Isolate a variable by using inverse operations which "undo" operations on the variable. Multiplication Division Multiplication

Balance An equation is like a balanced scale. To keep the balance, perform the same operation on both sides.

Solve the equation. Check your answer. Check It Out! Example 1 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. –6 = k – = k Check –6 = k – 6 –6 0 – 6 –6 To check your solution, substitute 0 for k in the original equation.

Remember that subtracting is the same as adding the opposite. When solving equations, you will sometimes find it easier to add an opposite to both sides instead of subtracting.

Solve –11 + x = 33. Check your answer. Check It Out! Example 2 Since –11 is added to x, add 11 to both sides. –11 + x = x = 44 Check –11 + x = 33 – To check your solution, substitute 44 for x in the original equation.

Solve –2.3 + m = 7. Check your answer. Now you try! Example 3 Since –2.3 is added to m, add 2.3 to both sides. –2.3 + m = m = 9.3 Check –2.3 + m = 7 – To check your solution, substitute 9.3 for m in the original equation.

Solve the equation. Check your answer. Example 4: Solving Equations by Using Division Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = To check your solution, substitute 12 for y in the original equation. 9y = 108 9(12) 108 Check 9y = 108

Solve the equation. Check your answer. Now you try! Example 5 Since c is multiplied by 4, divide both sides by 4 to undo the multiplication. 4 = c 16 To check your solution, substitute 4 for c in the original equation. 16 = 4c 16 4(4) Check 16 = 4c

Solve the equation. Example 6: Solving Equations by Using Multiplication Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j –8 To check your solution, substitute –24 for j in the original equation. –8 = j 3 –8 –24 3 Check –8 = j 3

Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. What about fractions?

Solve the equation. Example 7: Solving Equations That Contain Fractions w = 24 20 To check your solution, substitute 24 for w in the original equation. w =  Check w =  The reciprocal of is. Since w is multiplied by, multiply both sides by 20

Solve the equation. Example 8: You try this one = z 3 16 To check your solution, substitute for z in the original equation. 3 2 = z The reciprocal of is 8. Since z is multiplied by, multiply both sides by Check = z

A person's maximum heart rate is the highest rate, in beats per minute, that the person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find a person's age if the person's maximum heart rate is 185 beats per minute. Check It Out! Real Life Application #1

Check It Out! Application Continued a + r = 220 age added to 220 maximum heart rate is Write an equation to represent the relationship. – 185 a = 35 a = 220 Substitute 185 for r. Since 185 is added to a, subtract 185 from both sides to undo the addition. a + r = 220 A person whose maximum heart rate is 185 beats per minute would be 35 years old.

Example 4: Application #2 Write an equation to represent the relationship. Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 1 4 one-fourth times earnings equals college fund m = $1140 Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns.

Jeanne’s Problem Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

Variable Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem: Equation 17 + x = 68

To solve We can subtract 17 from both sides of the equation to find the value of x x = X = Answer: x = 51

So, Jeanne needs $51 to buy the game. This makes sense because most video games cost around $50.00