Question

Решить уравнение(х-7 5/8)+3 11/24=5 3/16

Answer 1

Ответ:

Пошаговое объяснение:

(х-7 5/8)+3 11/24=5 3/16

Х=5 3/16+7 5/8-3 11/24

Х=5 9/48+7 30/48-3 22/48

Х=9 17/48

Answer 2

To solve the equation, we need to simplify both sides and find the value of 'x'. Let's begin by performing the arithmetic operations step by step.

Step 1: Convert all the mixed numbers into improper fractions.

• For the mixed number '5 3/16,' the improper fraction will be (5 * 16 + 3) / 16 = 83 / 16.
• For the mixed number '3 11/24,' the improper fraction will be (3 * 24 + 11) / 24 = 83 / 24.

The equation becomes:

(x - 7 5/8) + 83/24 = 83/16

Step 2: Find a common denominator for both fractions on the left side, which is 24. Convert 7 5/8 to an improper fraction with the denominator of 24.

7 5/8 = (8 * 7 + 5) / 8 = 59 / 8

Now, the equation becomes:

(x - 59/8) + 83/24 = 83/16

Step 3: To eliminate the fractions, let's find a common denominator for the fractions on both sides, which is 24.

The right side already has a denominator of 16, so we need to convert 83/24 to have the same denominator:

83/24 = (24 * 3 + 11) / 24 = 83 / 24

Now, the equation becomes:

(x - 59/8) + 83/24 = 83/16

Step 4: Now, combine the fractions on the left side:

((24 * x - 24 * 59/8) + 83) / 24 = 83/16

Step 5: Simplify the expression on the left side:

(24x - 24 * 59/8 + 83) / 24 = 83/16

Step 6: Next, isolate 'x' by getting rid of the fraction on the left side. We do this by multiplying both sides by 24:

24 * (24x - 24 * 59/8 + 83) / 24 = 24 * (83/16)

Simplify:

24x - 24 * 59/8 + 83 = (24 * 83)/16

Step 7: Continue simplifying:

24x - 24 * 59/8 + 83 = 1248/16

Step 8: Convert the mixed number on the right side to an improper fraction:

1248/16 = (16 * 78) / 16 = 78

Now, the equation becomes:

24x - 24 * 59/8 + 83 = 78

Step 9: To isolate 'x,' get rid of the constant term (83) on the left side by subtracting it from both sides:

24x - 24 * 59/8 = 78 - 83 24x - 24 * 59/8 = -5

Step 10: Now, we'll isolate 'x' by getting rid of the fraction on the left side. We do this by adding 24 * 59/8 to both sides:

24x = -5 + 24 * 59/8

Step 11: Continue simplifying:

24x = -5 + 24 * 59/8 24x = -5 + 354/8

Step 12: Convert -5 to an improper fraction with a denominator of 8:

-5 = -5 * 8 / 8 = -40/8

Now, the equation becomes:

24x = -40/8 + 354/8

Step 13: Combine the fractions on the right side:

24x = (354 - 40) / 8

Step 14: Simplify the right side:

24x = 314 / 8

Step 15: Finally, solve for 'x' by dividing both sides by 24:

x = (314 / 8) / 24 x = 314 / (8 * 24) x = 314 / 192 x ≈ 1.6354

So, the solution to the equation is approximately x = 1.6354.