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1 2/5m + 16/25 = 2 5/6m - 3/5 - 3 1/2m

User Markm
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1 Answer

3 votes

Answer:

m = -0.6 or m = -3/5

Explanation:

Step 1: Convert 1 2/5, 2 5/6, and -3 1/2 (mixed numbers) to improper fractions:

  • Converting 1 2/5, 2 5/6 and -3 1/2 to improper fractions will make it easier when solving for m.
  • When converting mixed numbers to improper fractions, we keep the same denominator.
  • For the numerator, we multiply the whole number by the original denominator and add the original numerator.
  • For -3 1/2, we can leave off the negative and add it back at the end.
  • Since all three numbers are coefficients of the variable m, we can multiply the improper fractions by m.

Converting 1 2/5 to an improper fraction:

((1 * 5) + 2) / 5

(5 + 2) / 5

7/5m

Converting 2 5/6 to an improper fraction:

((2 * 6) + 5) / 6

(12 + 5) / 6

17/6m

Converting -3 1/2 to an improper fraction:

-(((3 * 2) + 1) / 2)

-((6 + 1) / 2)

-7/2m

Thus, our new equation with the improper fractions is given by:

7/5m + 16/25 = 17/6m - 3/5 - 7/2m

Step 2: Eliminate the fractions by finding the least common denominator (LCD):

  • The least common denominator (LCD) is the essentially the least common multiple (LCM) of the denominators.
  • Finding it allows us to clear all the fractions.
  • The least common denominator is 150.

Now we can eliminate the fractions by multiplying each fraction by 150 and simplifying:

150(7/5m + 16/25 = 17/6m - 3/5 - 7/2m)

1050/5m + 2400/25 = 2550/6m - 450/5 - 1050/2m

210m + 96 = 425m - 90 - 525m

Step 3: Combine like terms on the right-hand side:

210m + 96 = (425m - 525m) - 90

210m + 96 = -100m - 90

Step 4: Add 90 to both sides:

(210m + 96 = -100m - 90) + 90

210m + 186 = -100m

Step 5: Subtract 210m from both sides:

(210m + 186 = -100m) - 210m

186 = -310m

Step 6: Divide both sides by -310 to solve for m:

(186 = -310m) / -310

m = -0.6 or m = -3/5

Thus, m = -0.6 or -3/5.

You can use either the decimal answer or the fractional answer, depending on your personal preference.

Optional Step 7: Check the validity of the answer:

We can check that our answer is correct by plugging in -0.6 for m and seeing if we get the same answer on both sides:

7/5(-0.6) + 16/25 = 17/6(-0.6) - 3/5 - 7/2(-0.6)

-21/25 + 16/25 = -17/10 - 3/5 + 21/10

-5/25 = -23/10 + 21/10

-1/5 = -2/10

-1/5 = -1/5

-0.2 = -0.2

Thus, our answer is correct.

User Terrence M
by
8.3k points

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