cc math i standards unit 3 4.5 solving two ... - quest math · cc math i standards: unit 3 4.5...
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CC MATH I STANDARDS UNIT 3 4.5 SOLVING TWO-STEP EQUATIONS: PART 1
WARM UP: Solve part (a) equations, and then use that to find part (b) answers.
1a) 94
94 −
=+ r
2a) 21
53=−x
3a) 511 −=+− u
1b) What is 3r?
2b) What is x – 2?
3b) What is u + 18?
4a) 543 =− s
5a) 67=
b
6a) 1432
=t
4b) What is 2s?
5b) What is 14−b ? 5b) What is 7
t?
INTRODUCTION TO SOLVING TWO-STEP STEP EQUATIONS:
Find numbers that answer the following questions: 1) What can you double and then add 5 to get 13? 2) What can you triple and then subtract by 7 to
get -1? 3) You can triple and then subtract by 1 to get 29?
4) What can you double and then add -6 to get -16? 5) What can you double and then subtract from 9
to get 5? 6) What can you half and then add 9 to get 15?
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SOLVING TWO-STEP EQUATIONS: Verbal explanation by fill in the blanks
#1) 7m – 17 = 60 Step One: What minus 17 equals 60?
– 17 = 60 Step Two: What times 7 equals previous answer?
7 = #2) –2n – 25 = 13 Step One: What minus 25 equals 13?
– 25 = 13 Step Two: What times -2 equals previous answer?
-2 =
#3) 7 + 3x = 40 Step One: 7 plus what equals 40?
7 + = 40 Step Two: What times 3 equals previous answer?
3 =
#4) 12 + 5y = 27 Step One: 12 plus what equals 27?
12 + = 27 Step Two: What times 5 equals previous answer?
5 =
TWO-STEP EQUATIONS: Work Backwards
1) Find the VARIABLE. 2) Identify all operations. 3) In REVERSE ORDER of PEMDAS (SADMEP), cancel operations. 4) Use the same number and opposite operations
Operations: Operations: Operations: Operations: 1) 2y – 7 = 23 2) 8 + 6x = - 4 3) -5r - 18 = 12 4) 11 – 7x = 67
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PRACTICE: SOLVING TWO-STEP EQUATIONS 1. 2127 =−x 2. 2447 =−a 3. 3774 =−x 4. 993 =−y 5. y9835 −= 6. 32128 =− x 7. 5.65.32 =−y 8. 75250 += x 9. )18(62 −+=x 10. 749 +=− m 11. 6122 =+g 12. 8528 −=− y
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13. 1713 +=− h 14. 32713 −=+d 15. 5641 −=− x 16. 22310 =− x 17. 4727 =−y 18. 37512 =−− z 19. 2385 −=−n 20. r7325 +−= 21. 4026 =−x 22. 1443 =−y 23. 26)9(5 =−+x 24. )3(829 −+= y
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CC MATH I STANDARDS: UNIT 3 4.5 SOLVING TWO-STEP EQUATIONS: PART 2
WARM UP: Solve for the given variable. 1) 1953 =−z
2) 6720 += y
3) 2149 −=+− x
4) 16311 =−− m
5) 7215 +−= x
6) r61032 +=−
SOLVING 2-STEP EQUATIONS WITH FRACTIONS • Solve in reverse order of operations = SADMEP • FRACTIONS represent DIVISION statements. • Be careful for hidden parentheses when there are OPERATIONS in numerator
Option #1: NO OPERATIONS IN NUMERATOR
Option #2: OPERATIONS IN NUMERATOR
453
=−n
435=
−n
PRACTICE PROBLEMS
1) 293
−=−b
2) 6915
−=−r
3) 1064
−=−−t
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4) 5515
=+t
5) 6410
=−z
6) 729
=− p
7) 845
−=+y
8) 357=
+m 9) 9
215 −=− x
10) 634
−=−y
11) 534
=+−x
12) 17
12−=
− n
13) 32123
=+b
14) 62527
=− a
15) 5
732=
−s
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WORD PROBLEMS INVOLVING MULTI-STEP EQUATIONS: Write an equation for the problem below and then solve the equation.
1) The product of negative 4 and y increased by 11 is equivalent to -5.
2) Eight more than five times a number is negative 62.
3) 8 less than twice a number is twelve.
4) The product of 5 and x decreased by 7 is as much as 42.
5) How old am I if 400 reduced by 2 times my age is 244?
6) For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?
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7) Sarah won 40 super bouncy balls playing
horseshoes at her school's game night. Later, she gave two to each of her friends. She only has 8 remaining. How many friends does she have?
8) You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?
9) Two-thirds of a number minus six is –10
10) One-fourth of a number increased by 5 is as much as 3.
11) 3 fifths of a number less than 9 equals 2
12) 11 minus one-half of a number is -13.