Lesson #1: Solving for the Unknown with no Coefficients During this unit, we will be dealing with several terms: Variable a letter that is used to represent an unknown number Coefficient a number placed in front of a variable and is multiplied by the variable Constant a number found by itself in an equation 2x = 14 x = variable 2 = coefficient 14 = constant When solving for X (the unknown), keep the variable on the left side, and bring the constants to the right side by cancelling it out. To cancel out the constant, do the opposite of what is in the question, but make sure you do it to both sides of the equal sign. That means if you put 7 on the left side, you have to put it on the right side of the equal sign. What we are doing is combining similar terms. For example: X + 7 = 24 X + 7 7 = 24 7 X + 0 = 17 X = 17 Similar terms or also called like terms mean that two things are the same. For example X, 4X, 12X, and 7X are all terms and they are all the same type because they have the same variable. Other terms that are considerate the same are constants, for example: 6, 8, and 21 are all the same type of term even though the numbers are all different. When you have more than one similar term separated by the equal sign, they must be combined to make one term. Other examples: 5 + X = 14 X 6 = 26 X 12 = 12 5 5 + X = 14 5 X 6 + 6 = 26 + 6 X 12 + 12 = 12 + 12 0 + X = 9 X 0 = 32 X 0 = 24 X = 9 X = 32 X = 24
Assignment #1: Solving for the Unknown with no Coefficients Solve the following. 1) X + 7 = 13 11) 2 + X = 7 2) X 9 = 0 12) 9 + X = 4 3) X + 8 = 17 13) 14 + X = 7 4) 5 + X = 8 14) 6 + X = 2 5) 8 + X = 17 15) 7 + X = 18 6) X + 3 = 14 16) X 15 = 3 7) 8 + X = 3 17) 5 + X = 3 8) X + 7 = 11 18) X + 5 = 17 9) X 9 = 6 19) X + 3 = 16 10) 12 + X = 0 20) 10 + X = 14
Lesson #2: Solving for the Unknown with Coefficients When solving for X and dealing with coefficients, the same concept of doing the opposite still applies. Keep the variable on the left side, and bring the coefficient to the right side by cancelling it out. Remember that coefficients are multiplied by the variable, so you will use division to cancel out the coefficient. For example: 7X = 56 7 7 X = 56 7 X = 8 5X = 55 5 5 X = 55 5 X = 11 6X = 54 6 6 X = 54 6 X = 9
Assignment #2: Solving for the Unknown with Coefficients Solve the following. 1) 6X = 48 11) 4 + X = 11 2) 7X = 70 12) 9X = 27 3) 5X = 45 13) 2 + X = 5 4) 4X = 12 14) 5X = 12 5) 3X = 24 15) 6X = 36 6) 4X = 8 16) 6 + X = 17 7) 7X = 35 17) 7X = 42 8) 3X = 27 18) X 11 = 6 9) 5X = 15 19) 9X = 36 10) 5X = 30 20) 2 + X = 7
Lesson #3: Solving for the Unknown with Similar Terms We will now solve for X when there is more than one similar term on either side of the equal sign. Stay consistent and bring the coefficient and variable to the left and the constant to the left side. Let s look at some examples. 6X + 4 = 3X + 19 Bring similar terms together by cancelling out 6X + 4 4 = 3X 3X + 19 Combine similar terms by subtracting 6X 3X = 19 4 3X = 15 Cancel out the coefficient 3 3 X = 15 3 X = 5 5X 3 = 3X + 21 Bring similar terms together by cancelling out 5X 3 + 3 = 3X 3X + 21 Combine similar terms by subtracting and adding 5X 3X = 21 + 3 8X = 24 Cancel out the coefficient ( 8) ( 8) X = 24 ( 8) X = 3 With some questions, you might have to multiply first to get rid out of the brackets before combining similar terms. For example: Multiply first to get rid of the brackets 3(2X 7) = 9 6X 21 = 9 Cancel out constant by doing the opposite 6X 21 + 21 = 9 + 21 6X = 30 Cancel out the coefficient 6 6 X = 30 6 X = 5 4(X + 3) = 2X + 30 4X + 12 = 2X + 30 4X + 2X + 12 12 = 2X + 2X + 30 12 6X = 18 6 6 X = 18 6 X = 3
Assignment #3: Solving for the Unknown with Similar Terms Solve the following. 1) 19X = 10X + 90 6) 7(2X) = 140 2) 6(X 5) = 18 7) 9( 4 + X) = 36 3) 10 + 3X = 34 8) 10X = 2X + 24 4) 3X 4 = 2 4X 9) 6X = 20 + 2X 5) 7X + 6 = 20 10) 7X 10 = 53
11) 6X + 5 = 41 17) 2X + 7 = 3X + 17 12) 5 9X = 2 10X 18) 10X 5 = 45 13) 3X 9 = 5 4X 19) 3 + 5X = 4X + 2 14) 6X = 30 4X 20) 6 + 4X = 38 15) 10X 100 = 60 21) 10 + 3X = 22 16) 2( 2 + X) = 16 22) 11X = 4X + 42
23) 5X = 7X + 8 29) 9X + 10 = 17 10X 24) 10(10X) = 700 30) 4X 24 = 8 25) 4(X + 7) = 60 31) 10( 5 + X) = 20 26) 10( 2 + X) 50 32) 9(6X) = 540 27) 3X = 56 4X 33) 9(X + 3) = 45 28) 9X + 4 = 10X + 8 34) 10X 50 = 50
35) 7 9X = 10X + 11 41) 8 + 4X = 4 36) 3X + 2 = 6 + 2X 42) 4 + 4X = 12 37) 5X 4 = 41 43) 2( 5 + X) = 4 38) 8 + 5X = 23 44) 5X + 10 = 4X + 19 39) 2X + 4 = 3X + 13 45) 5X 7 = 13 40) 3 + 6X = 39 46) 4X 5 = 15
47) 8 + 10X = 108 51) 9X + 63 = 99 48) 10(X 4) = 50 52) 4X = 5X + 36 49) 48 + 6X = 36 53) X + 9 = 19 50) X = 9X + 100 54) 10X = 50
Solve the following. 1) 2X + 4 = 3X + 14 7) 4 + 3X = 28 2) 2 6X = 7X + 5 8) 6X + 3 = 7 + 5X 3) 0 = 2X + 18 9) 3 6X = 7 7X 4) 7(3 + X) = 70 10) 3(2X) = 30 5) 5 + 10X = 45 11) 4X + 9 = 3X + 13 6) 20 + 2X = 36 12) 10X = 2X + 40
13) 18X = 81 + 9X 19) 3X = 8X + 25 14) 4(10X) = 200 20) 3X = 2X + 30 15) X 5 = 3 2X 21) 2 + X = 1 16) 11X = 28 + 7X 22) 10 + X = 8 17) 4(4X) = 144 23) 2 + X = 4 18) 8(3X) = 216 24) 7 + X = 3
25) 10X = 80 31) 9 + X = 1 26) 4X = 20 32) 10X = 60 27) 8 + X = 12 33) X + 6 = 11 28) 8X = 40 34) 5X = 40 29) X + 3 = 6 35) 2X = 18 30) 9X = 81 36) 3X = 27
37) 9X = 63 43) 10 + 6X = 20 38) 9X = 45 44) 3(X 6) = 6 39) 5X 5 = 6X + 4 45) 16 + 4X = 4 40) 7(X + 2) = 56 46) 5 + 10X = 95 41) 2X + 12 = 30 47) 7X + 28 = 77 42) 8 6X = 4 7X 48) 4(8X) = 288
Solve the following. 1) 5X + 9(3X) = 5X + 135 6) 9 + 10X + 10(7X) = 10X + 709 2) 8X + 2(X + 2) = 22 + 8X 7) 5 + 9(10X) = 139 + 54X 3) 8 5X + 9(3X) = 5X = 143 8) 48X = 16( 9 + X) = 48X 64 4) 2X + 2( 8 + 5X) = 44 + 2X 9) 21(4X 10) = 105 + 63X 5) 7 + 7X + 10(10X) = 793 + 7X 10) 5 + 7X + 2(2X) = 29 + 7X
11) 50X + 40(X + 8) = 50X + 520 17) 4 + 9X + 10(9X) = 364 + 9X 12) 3 + 7X + 10(7X) = 7X + 627 18) 3 9X + 6(3X) = 9X + 141 13) 5(28 + 17X) = 50X + 315 19) 8 + 6X + 8(8X) = 6X + 504 14) 3X + 7( 9 + 3X) = 21 + 3X 20) 9 7X + 9(4X) = 7X + 261 15) 9( 7X + 3) = 153 81X 21) 28( 3 + 8X) = 84 + 196X 16) 10X + 5(56 + 8X) = 10X + 560 22) 8X + 60(5 + X) = 8X + 540
23) 4 + 8(7X) = 148 + 32X 29) 7( 42X 49) = 147 343X 24) 4(17X 20) = 28X + 120 30) 2X + 6(6X + 4) = 2X + 132 25) 3X + 20(X 8) = 3X + 20 31) 50X + 100(5 + X) = 50X + 1200 26) 4( 18 + 81X) = 288X + 180 32) 6X + 10(7 + X) = 6X + 110 27) 7(10 4X) = 280 49X 33) 6 3X + 7(7X) = 300 3X 28) 2(9X + 20) = 14X + 64 34) 7 + 5(7X) = 15X + 173
35) 2 2X + 5(5X) = 2X + 248 41) 91(39X) = 149058 36) 50(4 + 8X) = 350X + 350 42) 79(X 31) = 869 37) 81 + 48X = 4017 43) 71X 29 = 66 72X 38) 59 + 4X = 133 44) 57( 92 + X) = 3876 39) 15X + 765 = 825 45) 49X + 4361 = 7840 40) 19(X 48) = 646 46) 1653 + 57X = 285
47) 456 + 6X = 258 52) 51(38X) = 96900 48) 58 + 8X = 10 53) 65(3X) = 1755 49) 47X = 36X + 363 54) 93X + 22 = 1789 50) 32X 23 = 39 33X 55) 97 5X = 6X 61 51) 190 + 2X = 272 56) 48X + 21 = 3813