Question

(x+2 1/2)÷3/8-1,125=22 7/8​

Answer 1

Ответ:

Пошаговое объяснение:

(x+2 1/2)÷3/8-1,125=22 7/8​

(x+2 1/2)÷3/8=1,125+22 7/8​

(x+2 1/2)÷3/8=1 1\8+22 7/8​

(x+2 1/2)÷3/8=24

х+2 1\2=24*3\8

х+2 1\2=9

х=9-2 1\2

х=6 1\2

Answer 2

To solve the given equation, let's simplify the expression on the left-hand side step by step:

Step 1: Simplify the fraction inside the parentheses: x + 2 1/2 = x + 5/2

Step 2: Rewrite the expression with a common denominator: (x + 5/2) ÷ 3/8 - 1,125 = 22 7/8

Step 3: Convert the whole number and mixed number to improper fractions: 22 7/8 = 22 + 7/8 = (22 * 8 + 7) / 8 = 183/8

Step 4: Distribute the division operation over the addition: (x + 5/2) ÷ 3/8 = (x + 5/2) * 8/3

Step 5: Substitute the rewritten expression back into the equation: (x + 5/2) * 8/3 - 1,125 = 183/8

Step 6: Multiply the fractions: 8/3 times (x + 5/2) is (8 * (x + 5/2)) / 3

Step 7: Rewrite the equation with the new expression: (8 * (x + 5/2)) / 3 - 1,125 = 183/8

Step 8: Multiply 8 by (x + 5/2): (8x + 20)/3 - 1,125 = 183/8

Step 9: Convert the whole number to a fraction: 1,125 = 1,125/1

Step 10: Find a common denominator for the fractions: The common denominator for 3, 8, and 1 is 24.

Step 11: Adjust the fractions to have a common denominator of 24: [(8x + 20) * 8 - 1,125 * 3]/24 = (183 * 3)/24

Step 12: Simplify the numerator of the left side: (64x + 160 - 3,375)/24 = 549/24

Step 13: Combine like terms in the numerator: 64x - 3,215 = 549/24

Step 14: Simplify the fraction on the right side: 549/24 is an irreducible fraction.

Step 15: Multiply both sides of the equation by 24 to eliminate the denominator: 24 * (64x - 3,215) = 549

Step 16: Distribute the multiplication on the left side: 1,536x - 77,160 = 549

Step 17: Move the constant term to the right side: 1,536x = 549 + 77,160

Step 18: Add the numbers on the right side: 1,536x = 77,709

Step 19: Divide both sides by 1,536 to solve for x: x = 77,709 / 1,536

Step 20: Simplify the fraction on the right side: x ≈ 50.56

Therefore, the value of x that satisfies the equation (x + 2 1/2) ÷ 3/8 - 1,125 = 22 7/8 is approximately x ≈ 50.56.