Question

(2 7/8-x)+4 1/6=5 3/4​

Answer 1

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Answer 2

To solve the equation (2 7/8 - x) + 4 1/6 = 5 3/4, you can follow these steps:

Step 1: First, simplify the mixed numbers on both sides of the equation by converting them to improper fractions.

2 7/8 = (8 * 2 + 7) / 8 = 23/8 4 1/6 = (6 * 4 + 1) / 6 = 25/6 5 3/4 = (4 * 5 + 3) / 4 = 23/4

Now, the equation becomes:

(23/8 - x) + (25/6) = (23/4)

Step 2: To get rid of the fractions, find a common denominator for the fractions on the left side of the equation, which is 24. Multiply each term by 24 to clear the fractions:

24 * (23/8 - x) + 24 * (25/6) = 24 * (23/4)

This simplifies to:

(3 * 23 - 24x) + (4 * 25) = (6 * 23)

Step 3: Continue simplifying the equation:

(69 - 24x) + 100 = 138

Step 4: Now, combine like terms on the left side of the equation:

(69 + 100) - 24x = 138

169 - 24x = 138

Step 5: To isolate the variable x, subtract 169 from both sides of the equation:

-24x = 138 - 169

-24x = -31

Step 6: Finally, divide both sides by -24 to solve for x:

x = (-31) / (-24)

x = 31/24

So, the solution to the equation is:

x = 31/24

You can also express this as a mixed number:

x = 1 7/24