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Solve each equation, if possible. $$ \frac{1}{3} …

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105 Problem 106 Problem 107 Problem 108 Problem 109 Problem 110 Problem 111 Problem 112 Problem 113 Problem 114 Problem 115 Problem 116 Problem 117 Problem 118 Problem 119 Problem 120 Problem 121 Problem 122 Problem 123 Problem 124

Problem 71 Medium Difficulty

Solve each equation, if possible.
$$
\frac{1}{6} y+\frac{1}{4} y=-1
$$

Answer

$-\frac{12}{5}$

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 2

More about Solving Equations

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Equations and Inequalities

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Video Transcript

So any time you see fractions or decimals, you kind of want to just get rid of them. They make everything easier if you could just clear it out and have a one level problem. So what I'm gonna do is look at my denominators, which are six and four. And I'm looking for the least common denominator. The smallest thing that six and four go into. People are quick to say 24 but there is something smaller, which is 12. So what I'm gonna do is multiply every single term by 12. The idea of that is here six goes into 12 twice. So I have two times. One times why, which is just too. Why, plus, here four goes into 12 3 times and I have three times, one times why or three way. And here I just get negative 12. Okay, let's collect like terms. So I have five. Why equals negative 12. And for my final step, I need why by itself. So we will undo the multiplication by dividing, and I get why equals negative 12 5th Okay, we want to check this work so I'll go ahead and plug in negative 12 5th everywhere I see a why? To see if this does indeed equal negative one six goes into 12 twice. So this is negative. 2/5. Four goes into 12 3 times. So this is negative. 3/5. Hopefully you can see this, but I have negative two minus three. All over five to negative 5/5. Negative one does equal negative one. So this is why negative 12.

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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