Question

5/9x-7/4 x+17/18x=-1/4

Answer 1

40/72х-126/72х+68/72х=-18/72
-18/72х=-18/72
х=1

Answer 2

To solve the equation 5/9x - 7/4 + x + 17/18x = -1/4, we can follow these steps:

Step 1: Combine like terms on the left side of the equation. We can combine the terms with x by adding the coefficients: (5/9 + 1 + 17/18)x - 7/4 = -1/4

Step 2: Find a common denominator. To add fractions, we need a common denominator. In this case, the least common denominator (LCD) is 36. Let's rewrite the equation with the common denominator: [(20 + 36 + 17)/36]x - 7/4 = -1/4

Step 3: Simplify the coefficients. Now, let's simplify the equation further: (73/36)x - 7/4 = -1/4

Step 4: Move the constant terms to the right side of the equation. To isolate the variable, we need to move the constant term (-7/4) to the right side of the equation by adding it to both sides: (73/36)x = -1/4 + 7/4

Simplifying the right side: (73/36)x = 6/4

Step 5: Simplify the right side further. (73/36)x = 3/2

Step 6: Multiply both sides by the reciprocal of the coefficient of x. To solve for x, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which is (36/73): [(36/73) * (73/36)]x = (3/2) * (36/73)

Simplifying: x = (3/2) * (36/73)

Step 7: Simplify the right side. To get the final answer for x, we multiply the fractions: x = 108/146

Step 8: Simplify the fraction, if possible. If we can simplify the fraction 108/146, we can divide the numerator and denominator by their greatest common divisor, which is 2: x = 54/73

Therefore, the solution to the equation 5/9x - 7/4 + x + 17/18x = -1/4 is x = 54/73.