Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Solve a Two-Step Equation Example 2:Solve Two-Step Equations Example 3:Solve Two-Step Equations Example 4:Solve Two-Step Equations Key Concept:Solving Two-Step Equations Example 5:Real-World Example: Solve Two-Step Equations Five-Minute Check

Main Idea/Vocabulary Solve two-step equations. two-step equation

NGSSS MA.7.A.3.3 Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients. Also addresses MA.7.A.3.2.

Example 1 Solve a Two-Step Equation Solve 4x + 3 = 19. Check your solution. 4x + 3= 19Write the equation. – 3= – 3Undo the addition first by subtracting 3 from each side. 4x=16 x= 4Simplify. Division Property of Equality Answer: The solution is 4.

Example 1 Solve a Two-Step Equation 4x + 3= 19Write the original equation. 19= 19The sentence is true. Check 4(4) + 3= 19Replace x with 4. ?

Example 1 CYP Solve 3z + 1 = 4. Check your solution. A.0 B.1 C. D.8

Example 2 Solve 6 + 5y = 26. Check your solution. Solve Two-Step Equations 6 + 5y=26Write the equation. – 6= – 6Undo the addition first by subtracting 6 from each side. 5y=20 y= 4Simplify. Division Property of Equality Answer: The solution is 4.

Example 2 Solve Two-Step Equations 6 + 5y= 26Write the original equation. 26= 26The sentence is true. Check 6 + 5(4)= 26Replace y with 4. ?

Example 2 CYP Solve 7 + 3y = 16. Check your solution. A.27 B.26 C.–3 D.3

Example 3 Solve Two-Step Equations Solve −3c + 9 = 3. Check your solution. –3c + 9=3Write the equation. – 9= – 9Undo the addition first by subtracting 9 from each side. –3c=–6 c= 2Simplify. Division Property of Equality Answer: The solution is 2.

Example 3 Solve Two-Step Equations –3c + 9= 3Write the original equation. 3= 3The sentence is true. Check –3(2) + 9= 3Replace c with 2. ?

Example 3 CYP Solve −d + 5 = 2. Check your solution. A.7 B.–7 C.3 D.

Example 4 Solve Two-Step Equations Solve Check your solution. – 6=– 6Undo the addition first by subtracting 6 from each side. –18= tSimplify. –6= t 1 3 Multiplication Property of Equality (3)(–6)=(3)t 1 3 Write the equation. Answer: The solution is –18.

Example 4 Solve Two-Step Equations Write the original equation. 0=0The sentence is true. Check ? Replace t with –18. 0=6 + (–18) 1 3

Example 4 CYP Solve Check your solution. A.20 B.16 C.12 D.3

Key Concept

Example 5 FINANCIAL LITERACY Luis’s cell phone plan costs $39 per month. Text messages cost an additional $0.15 each. If Luis’s cell phone bill last month totaled $55.05, how many text messages did he send? Solve Two-Step Equations

Example 5 Solve Two-Step Equations

Example 5 Solve Two-Step Equations t = 55.05Write the equation. – 39 = – 39Subtract 39 from each side. t = 107Simplify. Division Property of Equality Answer: Luis sent 107 text messages.

Example 5 Solve Two-Step Equations t=55.05Write the original equation. Check ? (107)=55.05Replace t with =55.05 ?

Example 5 CYP TENNIS Shannon’s tennis club membership costs $20.00 per month. In addition, she pays $8.00 for court rental every time she plays. If her bill for this month was $52.00, how many times did she play tennis? A.24 times B.9 times C.4 times D.3 times

Solve 4x + 8 = 32. Five Minute Check 1 A.6 B.10 C.20 D.96

Solve 15 – 3a = 45. Five Minute Check 2 A.–10 B.10 C.20 D.90

Solve –9 + 7x = 68. Five Minute Check 3 A.70 B.52 C.11 D.

Solve –18 = –2m –68. Five Minute Check 4 A.52 B.43 C.25 D.–25

Four less than six times a number is 32. Find the number. Five Minute Check 5 A.22 B.6 C.–6 D.

Daryl can cut 3 lawns in an hour. How many hours will it take him to cut 27 lawns? Five Minute Check 6 A.30 hours B.24 hours C.15 hours D.9 hours