Question

3/4(x+2)+2/3(x-1)=5​

Answer 1

$\frac{3}{4} (x + 2) + \frac{2}{3} (x - 1) = 5 \\\\ \frac{3}{4} x + \frac{3}{2} + \frac{2}{3} x - \frac{2}{3} = 5 \\ \\ \frac{3}{4} x + \frac{5}{6} + \frac{2}{3} x = 5 \\ \\ 9x + 10 + 8x = 60 \\ \\ 17x + 10 = 60 \\ \\ 17x = 60 - 10 \\ \\ 17x = 50 \\ \\ x = \frac{50}{17} \\ \\ x = 2 \frac{16}{17}$

Answer 2

To solve the equation 3/4(x + 2) + 2/3(x - 1) = 5, we'll follow the steps below:

Step 1: Distribute the fractions Multiply 3/4 by (x + 2) and 2/3 by (x - 1):

(3/4)(x + 2) + (2/3)(x - 1) = 5

Expanding:

(3/4)x + 3/2 + (2/3)x - 2/3 = 5

Step 2: Combine like terms Combine the terms with x and the constant terms separately:

[(3/4)x + (2/3)x] + [3/2 - 2/3] = 5

To add the fractions, we need a common denominator, which is 12. So we'll convert them:

[(9/12)x + (8/12)x] + [(9/6) - (4/6)] = 5

Simplifying:

[(17/12)x] + [(5/6)] = 5

Step 3: Get rid of the fractions To eliminate the fractions, we'll multiply the entire equation by the least common multiple (LCM) of the denominators, which is 12:

12 * [(17/12)x] + 12 * [(5/6)] = 12 * 5

Canceling out the denominators:

17x + 10 = 60

Step 4: Isolate the variable To isolate the variable x, we'll subtract 10 from both sides:

17x = 60 - 10 17x = 50

Divide both sides by 17:

x = 50/17

So the solution to the equation 3/4(x + 2) + 2/3(x - 1) = 5 is x = 50/17.