Question

5/8 * (x-2)- 2/3 *(x+2) = -1

Answer 1

$\frac{5}{8} \times (x - 2) - \frac{2}{3} \times (x + 2) = - 1 \\ \frac{5}{8} x - \frac{5}{4} - \frac{2}{3} x - \frac{4}{3} = - 1 \\ \frac{5}{8} x - \frac{31}{12} - \frac{2}{3} x = - 1 \\ 15x - 62 - 16x = - 24 \\ - x - 62 = - 24 \\ - x = - 24 + 62 \\ - x = 38 \\ x = - 38$

Answer 2

$\frac{5}{8} (x - 2) - \frac{2}{3} ( x+ 2) = - 1 \\ x( \frac{5}{8} - \frac{2}{3} ) - \frac{5}{4} - \frac{4}{3} = - 1 \\ - \frac{x}{24} - \frac{31}{12} = - 1 \\ - \frac{x}{24} = \frac{19}{12} \\ x = - 2 \times 19 = - 38$

Answer 3

To solve the equation 5/8 * (x - 2) - 2/3 * (x + 2) = -1, follow these steps:

Step 1: Clear the fractions in the equation by multiplying both sides by the least common multiple (LCM) of the denominators, which is 24. This will get rid of the fractions:

24 * [5/8 * (x - 2) - 2/3 * (x + 2)] = 24 * -1

Step 2: Distribute the 24 on the left side of the equation to eliminate the fractions:

(24 * 5/8) * (x - 2) - (24 * 2/3) * (x + 2) = -24

Step 3: Simplify the fractions within the equation:

(3 * 5) * (x - 2) - (4 * 2) * (x + 2) = -24

Step 4: Continue simplifying:

15x - 30 - 8x - 16 = -24

Step 5: Combine like terms on both sides of the equation:

(15x - 8x) - (30 + 16) = -24

7x - 46 = -24

Step 6: Add 46 to both sides of the equation to isolate the variable term:

7x - 46 + 46 = -24 + 46

7x = 22

Step 7: Finally, divide both sides by 7 to solve for x:

7x/7 = 22/7

x = 22/7

So, the solution to the equation is:

x = 22/7