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|2x+3/4|=5 6/7
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User Jeremycg
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1 Answer

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Answer: x = 143/56 and x = -185/56.

Explanation:

Case 1: (2x + 3/4) is positive

2x + 3/4 = 5 6/7

First, convert the mixed fraction 5 6/7 to an improper fraction:

5 6/7 = 41/7

Now solve for x:

2x + 3/4 = 41/7

Subtract 3/4 from both sides:

2x = 41/7 - 3/4

Find a common denominator for 7 and 4, which is 28:

2x = (4 * 41)/(4 * 7) - (3 * 7)/(3 * 4)

2x = 164/28 - 21/28

2x = (164 - 21)/28

2x = 143/28

Divide both sides by 2:

x = 143/56

Case 2: (2x + 3/4) is negative

(2x + 3/4) = 5 6/7

Again, convert the mixed fraction to an improper fraction:

5 6/7 = 41/7

Now solve for x:

(2x + 3/4) = 41/7

Distribute the negative sign:

-2x - 3/4 = 41/7

Add 3/4 to both sides:

-2x = 41/7 + 3/4

Find a common denominator for 7 and 4, which is 28:

-2x = (4 * 41)/(4 * 7) + (3 * 7)/(3 * 4)

-2x = 164/28 + 21/28

-2x = (164 + 21)/28

-2x = 185/28

Divide both sides by -2:

x = -185/56

So, the solutions for the equation |2x + 3/4| = 5 6/7 are x = 143/56 and x = -185/56.

User EK Chhuon
by
8.7k points

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