Question

24 3/4-(x-15 1/4) = 4 1/4

Answer 1

Ответ:

Пошаговое объяснение:

А это ответ ?

Answer 2

To solve the equation, we'll first simplify both sides and then isolate the variable (x).

Step 1: Simplify the equation on the left-hand side. To simplify the left-hand side, we'll first deal with the parentheses.

24 3/4 - (x - 15 1/4) can be rewritten as 24 3/4 - x + 15 1/4.

Step 2: Combine the whole numbers and fractions. 24 3/4 - x + 15 1/4 can be simplified as (24 + 15) + (3/4 - 1/4) - x, which is equal to 39 + (3/4 - 1/4) - x.

Step 3: Calculate the fractions. 3/4 - 1/4 equals 2/4, which simplifies to 1/2. So, we get 39 + 1/2 - x.

Step 4: Convert 39 to a fraction with the same denominator as 1/2 (which is 2/2). 39 can be written as 39/1, and to have a common denominator with 1/2, we multiply both the numerator and denominator of 39/1 by 2.

39/1 * 2/2 = 78/2.

Now, the equation becomes 78/2 + 1/2 - x.

Step 5: Combine the fractions and simplify further. 78/2 + 1/2 equals (78 + 1) / 2, which is 79/2.

The equation now becomes 79/2 - x.

Step 6: Set the left-hand side equal to the right-hand side. So, the equation becomes:

79/2 - x = 4 1/4.

Step 7: Convert 4 1/4 to a fraction. 4 1/4 can be written as 4 + 1/4, which is equal to 16/4 + 1/4, making it 17/4.

Now, the equation becomes:

79/2 - x = 17/4.

Step 8: Isolate the variable (x) on one side of the equation. To do this, we need to move 79/2 to the other side of the equation.

Subtract 79/2 from both sides:

79/2 - 79/2 - x = 17/4 - 79/2.

On the left-hand side, 79/2 - 79/2 cancels out, leaving us with:

-x = 17/4 - 79/2.

Step 9: Convert 17/4 to a fraction with the same denominator as 2. To have a common denominator with 2, we multiply both the numerator and denominator of 17/4 by 2.

17/4 * 2/2 = 34/8.

The equation now becomes:

-x = 34/8 - 79/2.

Step 10: Simplify the right-hand side. 34/8 - 79/2 can be converted to have a common denominator:

34/8 - 79/2 = 34/8 - 4 * (79/8).

Now, the equation becomes:

-x = 34/8 - 316/8.

Step 11: Combine the fractions. -316/8 + 34/8 equals (-316 + 34) / 8, which is -282/8.

The equation now becomes:

-x = -282/8.

Step 12: Reduce the fraction on the right-hand side. -282/8 can be simplified further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2.

-282/8 = -141/4.

The equation becomes:

-x = -141/4.

Step 13: Solve for x. To solve for x, we need to isolate x on one side of the equation. To do this, we can multiply both sides by -1 (since a negative multiplied by a negative becomes positive):

(-1) * (-x) = (-1) * (-141/4).

This simplifies to:

x = 141/4.

So, the solution for the equation is:

x = 141/4 or x = 35 1/4.