Main Idea and New Vocabulary NGSSS Key Concept: Subtraction Property of Equality Example 1: Solve an Addition Equation Key Concept: Addition Property of Equality Example 2: Real-World Example Example 3: Solve a Subtraction Equation Five-Minute Check Lesson Menu

Solve equations using the Subtraction and Addition Properties of Equality. inverse operations Main Idea/Vocabulary

Preparation for MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable. NGSSS

Key Concept

Solve an Addition Equation Solve 7 = 15 + c. Check your solution. Method 1 Use the vertical method. 7 = 15 + c Write the equation. – 15 = – 15 Subtraction Property of Equality –8 = c Method 2 Use the horizontal method. 7 = 15 + c Write the equation. 7 – 15 = 15 + c – 15 Subtraction Property of Equality –8 = c Example 1

Solve an Addition Equation Answer: The solution is –8. Check 7 = 15 + c Write the original equation. 7 = 15 + (–8) Replace c with –8. Is this sentence true? ? 7 = 7 The sentence is true.  Example 1

Solve 9 + t = –4. A. –13 B. –5 C. 5 D. 13 Example 1 CYP

Key Concept 2

h + (–6) = 2 Write the equation. OCEANOGRAPHY At high tide, the top of a coral formation is 2 feet above the surface of the water. This represents a change of –6 feet from the height of the coral above the water at low tide. Write and solve an equation to determine h, the height of the coral above the water at low tide. Let h represent the height of the coral at high tide. So, h + (–6) = 2. h + (–6) = 2 Write the equation. + 6 = + 6 Addition Property of Equality h = 8 Simplify. Example 2

Answer: The height of the coral at low tide is 8 feet. Example 2

TEMPERATURE The temperature at 11:00 P. M. was 54°F TEMPERATURE The temperature at 11:00 P.M. was 54°F. This represents a change of –8° from the temperature at 9:00 P.M. Write and solve an equation to determine t, the temperature at 9:00 P.M. A. 54 – 8 = t; 46°F B. 54 + t = 8; –46°F C. –8t = 54; –6.75°F D. t + (–8) = 54; 62°F Example 2 CYP

Solve a Subtraction Equation Solve –5 = z – 16. Method 1 Use the vertical method. –5 = z – 16 Write the equation. + 16 = + 16 Addition Property of Equality 11 = z Method 2 Use the horizontal method. –5 = z – 16 Write the equation. –5 + 16 = z – 16 + 16 Addition Property of Equality 11 = z Example 3

Solve a Subtraction Equation Answer: The solution is 11. Example 3

Solve r – 2 = 14. A. –12 B. –7 C. 12 D. 16 Example 3 CYP

Solve −3 + b = −7. Check your solution. A. –10 B. −4 C. 3 D. 4 Five Minute Check 1

Solve c − 13 = 2. Check your solution. A. –15 B. –11 C. 11 D. 15 Five Minute Check 2

Solve x + 4 = 9. Check your solution. A. –5 B. 5 C. 13 D. 36 Five Minute Check 3

Solve 28 = −11 + b. Check your solution. A. 39 B. 17 C. –17 D. –39 Five Minute Check 4

If you increase a number by 9, the result is 26 If you increase a number by 9, the result is 26. Write and solve an equation to find the number. A. n + 9 = 26; n = 17 B. 9n = 26; n = 2.8 C. n – 26 = 9; n = 35 D. = 26; n = 234 __ n 9 Five Minute Check 5

Pam opened a checking account with $200 Pam opened a checking account with $200. Then she wrote a check for $125. What is the current balance in Pam’s checking account? A. −$33 B. $75 C. $83 D. $325 Five Minute Check 6