Question

11 2/3 x - 5 1/6 = 3 3/4 + 2 3/4 x

Answer 1

Ответ:

переводим в неправильную дробь

35/3х-31/6=15/4+11/4х

умножим обе части равенства на 12

/ это дробная черта.

140х-62=42+33х

х влево, числа вправо

140х-33х=45+62

107х=107

х=1

х=107÷107

Answer 2

To solve the equation, we need to isolate the variable (x) on one side. Let's solve it step by step:

Given equation: 11 2/3x - 5 1/6 = 3 3/4 + 2 3/4x

Step 1: Convert all mixed numbers to improper fractions.

• 11 2/3 = (3 * 11 + 2) / 3 = 35/3
• 5 1/6 = (6 * 5 + 1) / 6 = 31/6
• 3 3/4 = (4 * 3 + 3) / 4 = 15/4
• 2 3/4 = (4 * 2 + 3) / 4 = 11/4

Substitute these values back into the equation:

(35/3)x - (31/6) = (15/4) + (11/4)x

Step 2: Get rid of fractions by multiplying through by the least common multiple (LCM) of the denominators, which is 12 (since 3, 6, and 4 all divide evenly into 12):

12 * (35/3)x - 12 * (31/6) = 12 * (15/4) + 12 * (11/4)x

Simplify:

140x - 62 = 45 + 33x

Step 3: Move the terms involving x to one side of the equation and constants to the other side:

140x - 33x = 45 + 62

Simplify:

107x = 107

Step 4: Solve for x:

x = 107 / 107

x = 1

So, the solution to the equation is x = 1.