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

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

Solving One Step Equations

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

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.

Isolate a variable by using inverse operations which "undo" operations on the variable. Addition Subtraction Subtraction Addition Multiplication Division Division Multiplication

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

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

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.

–11+ x = 33 Check Check It Out! Example 2 Solve –11+x = 33. Check your answer. –11+x = 33 +11+11 Since –11 is added to x, add 11 to both sides. x = 44 To check your solution, substitute 44 for x in the original equation. –11 + 4433 3333 

–2.3+ m = 7 Check Now you try! Example 3 Solve –2.3+m = 7. Check your answer. –2.3+m = 7 +2.3+ 2.3 Since –2.3 is added to m, add 2.3 to both sides. m = 9.3 To check your solution, substitute 9.3 for m in the original equation. –2.3 + 9.37 77 

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

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

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

What about fractions? 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.

6 5 6 5 6 5 6 5 The reciprocal of is . Since w is multiplied by , multiply both sides by . 5 w = 20 Check 6 20 Example 7: Solving Equations That Contain Fractions Solve the equation. 5 w= 20 6 w = 24 To check your solution, substitute 24 for w in the original equation. 2020 

3 2 1 3 3 8 1 1 3 16 16 8 8 2 The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. = z 3 16 1 Check = z To check your solution, substitute for z in the original equation. 8 Example 8: You try this one Solve the equation. 3 = z 16 

Check It Out! Real Life Application #1 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.

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

1 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. 4 Example 4: Application #2 one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns. m = $1140

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. 17 -17 + x = 68 -17 X = 68 - 17 Answer: x = 51

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

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