Question

2 1\8 + 15\16x + 1 3\4x + 4\7 = 4 3\14

Answer 1

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Answer 2

To solve the equation, we need to combine like terms and then isolate the variable (x) on one side of the equation. Let's proceed step-by-step:

Step 1: Combine the "x" terms on the left side: 15/16x + 1 3/4x = (15/16 + 7/4)x

Step 2: Find the common denominator for the coefficients of "x": The common denominator for 16 and 4 is 16.

Step 3: Convert all the fractions to have a denominator of 16: 15/16 + 7/4 = (15/16) + (7/4) = (15/16) + (7 * 4/4) = (15/16) + (28/16) = (15 + 28)/16 = 43/16

So, the left side of the equation becomes: (43/16)x + 4/7

Step 4: Combine the constants on the left side: 2 1/8 + 4/7 = (2 * 8 + 1)/8 + 4/7 = (17/8) + (4/7)

Step 5: Find the common denominator for 8 and 7: The common denominator for 8 and 7 is 56.

Step 6: Convert all the fractions to have a denominator of 56: (17/8) + (4/7) = (17 * 7/8 * 7) + (4 * 8/7 * 8) = (119/56) + (32/56) = (119 + 32)/56 = 151/56

So, the left side of the equation becomes: 151/56

The equation now becomes: (43/16)x + 4/7 = 151/56

Step 7: Isolate the "x" term: Subtract 4/7 from both sides of the equation: (43/16)x = 151/56 - 4/7

Step 8: Find the common denominator for 56 and 7: The common denominator for 56 and 7 is 56.

Step 9: Convert all the fractions to have a denominator of 56: 151/56 - 4/7 = (151 * 1/56 * 1) - (4 * 8/7 * 8) = (151/56) - (32/56) = (151 - 32)/56 = 119/56

So, the equation now becomes: (43/16)x = 119/56

Step 10: Isolate "x" by multiplying both sides by the reciprocal of (43/16): x = (119/56) * (16/43)

Step 11: Simplify the right side: x = (119 * 16) / (56 * 43) = 1904 / 2408

Step 12: Reduce the fraction, if possible: x = 476 / 602

Step 13: Divide the numerator and denominator by their greatest common divisor (GCD) to get the simplest form: x = 238 / 301

Thus, the value of "x" in the given equation is 238/301.