Question

5 1/14-1 2/7x =2 3/4

Answer 1

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Answer 2

To solve the equation 5 1/14 - 1 2/7x = 2 3/4, we can follow these steps:

Step 1: Convert mixed numbers to improper fractions. 5 1/14 = (5 * 14 + 1) / 14 = 71 / 14 1 2/7 = (1 * 7 + 2) / 7 = 9 / 7 2 3/4 = (2 * 4 + 3) / 4 = 11 / 4

The equation becomes: (71/14) - (9/7)x = 11/4

Step 2: Find a common denominator for the fractions involved. The least common multiple (LCM) of 14, 7, and 4 is 28.

Multiply each fraction by the appropriate factor to make the denominators equal to 28: (71/14) * (2/2) = 142/28 (9/7) * (4/4) = 36/28 (11/4) * (7/7) = 77/28

The equation becomes: 142/28 - (36/28)x = 77/28

Step 3: Simplify the equation by subtracting (36/28)x from both sides. 142/28 - (36/28)x = 77/28 142/28 - 36/28x = 77/28

Step 4: Combine like terms on the left side of the equation. (142 - 36x) / 28 = 77/28

Step 5: Multiply both sides of the equation by the reciprocal of the fraction on the left side to eliminate the denominator. 28 * (142 - 36x) / 28 = 28 * (77/28) 142 - 36x = 77

Step 6: Solve for x. 142 - 36x = 77 -36x = 77 - 142 -36x = -65 x = (-65) / (-36) x ≈ 1.806

Therefore, the solution to the equation 5 1/14 - 1 2/7x = 2 3/4 is approximately x ≈ 1.806.