Math 7 NOTES (4.1) Name ______________________ Block ____ Solving One-Step Equations (SOL 7.14) The GOAL of solving an equation _______________________________________________________________ To do this you need to _________ what was done to the variable, using _______________________________. State the INVERSE OPERATIONS o Add 23 ______________________________ _____ o Subtract 18 ___________________________________ o Multiply by –15 ___________________________________ o Divide by 8 ___________________________________ Addition & Subtraction Equations: Example 1: Solve y 3 10 Example 2: y 3 10 Where is the variable? y 3 10 ___ ___ What was done to it? How can I undo that? Apply to BOTH sides. Simplify (Solve) CHECK: CHECK: y 3 10 ____ 3 ≟ 10 ____ 10 –2 = y – 7 SOLVE: SOLVE: y ____ Solve Write original equation. Substitute ____ for y. Did my solution make the equation true? Solve each equation. Check your solution. Solve a 6 17 3x2 Check here: Solve b 17 12 y 4 6 Check here: Multiplication & Division Equations: Example 3: Solve 8x = 56. Example 4: Solution: Solve 𝒂 𝟓 = 12 Solution: 8x = 56 𝑎 Where is the variable? What is done to it? 8x = _56_ = 12 5 How can I undo that? 𝑎 • = 12 • 5 Apply to both sides. x = _____ a = _____ Solve/Simplify Check: Check: 8x = 56 Write original equation. 8(___) ≟ 56 Substitute for variable. ____ 56 Is it true? 𝑎 5 ( = 12 ) 5 = 12 _____ = 12 Let’s Practice!! Solve each equation. Check your solution. Solve –3a 18 Check here: Solve 𝑏 −4 4 𝑓 12 48 6y 3 121 11a 𝑔 =7 −7 Check here: ______________________________ (Reciprocals): When multiplied, the product is one!! Multiply each number by its reciprocal. 𝟏 𝟓 𝟑 𝟕 𝟑 Solve 𝟓 − t6 𝟐 8 𝟓 Solve 𝟐 𝟕 t8 The coefficient of t is _____. The reciprocal of 3 5 𝟑 𝟓 is ____. t6 Multiply each side by the Multiplicative Inverse. t ____. Simplify. t = ____. Solve. Solve each equation. 1 7 t3 1 9 t–6 − 4 5 t8 − 3 5 t –6 Review Time! (–4)3x –5(7x) 2 (–x) –8(–4x) (–2)7a (–9x)(–4) –2m (5) –5 (–3d) 5a(3a) –6a(4a) 6a(-4a) (–8a)(–3a) Evaluate (4 + 7)2 − (24 – 3) −|5(-12)| -42 + (-4)2 Simplify 6 (y – 2=3) 4(7 – n) –5(s – 5) –10(3 – p) Translate each verbal phrase into an algebraic expression or equation. $15 off the original price is $78. 20 more than some number is equal to 92. Vocabulary Check: Operations that “undo” each other are called _____________________________ A mathematical sentence that contains an equal sign is an ____________________ A _______________________ is a number multiplied by a variable in an expression or equation. A ______________________ is a symbol, usually a letter, used to represent an unknown number. Math 7 HOMEWORK (4.1) 1. Solve the equations. Check your solutions. Solve Check here: 15 = w + 4 –3b = 21 𝑎 =5 −7 Solve Check here: a – 2 = 10 1 3 n = –13 3 7 n = 24 4x = -24 –8 = b – 5 𝑎 = –11 s +4 = 12 –7s = 49 15h = –75 −9 Write each verbal sentence as an algebraic equation. Solve the equations. 2. The sum of a number and 16 is equal to –45. 3. The product of –6 and m is 216. 4. The difference of x and 25 is 57. 5. The quotient of z and –10 is equal to 32. Translate and solve: 6. Six less than a number is eighteen. __________________________________________ 7. The number of members divided by 6 is 15. __________________________________________ Use the Distributive Property to rewrite and simply each expression. 8. 6(z + 4) 9. –7(c + 2) 10. (d + 5)9 11. (h + 8)(–3)