Rút gọn các biểu thức sau đây

To solve these equations, we will simplify and isolate the variable x.

1) 16/(1/2)x + (1/6)x(x-2) = 3/4 - 2x

First, let's simplify the equation:

16/(1/2)x = 32x
(1/6)x(x-2) = (1/6)x^2 - (1/3)x

Now, substitute the simplified expressions back into the equation:

32x + (1/6)x^2 - (1/3)x = 3/4 - 2x

Multiply the entire equation by 12 to eliminate the fractions:

384x + 2x^2 - 4x = 9 - 24x

Combine like terms:

2x^2 + 376x - 9 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = 376, and c = -9. Plugging these values into the formula:

x = (-376 ± √(376^2 - 4(2)(-9))) / (2(2))
x = (-376 ± √(141376 + 72)) / 4
x = (-376 ± √141448) / 4
x = (-376 ± 376.5) / 4

This gives us two possible solutions:

x1 = (-376 + 376.5) / 4 = 0.125
x2 = (-376 - 376.5) / 4 = -188.125

Therefore, the solutions to the equation are x = 0.125 and x = -188.125.

2) 19/(5/12)x + 3 = 1/3 - (7/12)x

First, let's simplify the equation:

19/(5/12)x = (19/5)(12/5)x = 228x/25
1/3 - (7/12)x = (4/12) - (7/12)x = (4 - 7x)/12

Now, substitute the simplified expressions back into the equation:

228x/25 + 3 = (4 - 7x)/12

Multiply the entire equation by 300 to eliminate the fractions:

912x + 900 = 100 - 175x

Combine like terms:

1087x = -800

Divide both sides by 1087:

x = -800/1087

Therefore, the solution to the equation is x ≈ -0.736.

3) 20/(1/2)x + 5/2 = (7/2)x - 3/4

First, let's simplify the equation:

20/(1/2)x = 40x
(7/2)x - 3/4 = (14/4)x - 3/4 = (14x - 3)/4

Now, substitute the simplified expressions back into the equation:

40x + 5/2 = (14x - 3)/4

Multiply the entire equation by 4 to eliminate the fractions:

160x + 10 = 14x - 3

Subtract 14x from both sides:

146x + 10 = -3

Subtract 10 from both sides:

146x = -13

Divide both sides by 146:

x = -13/146

Therefore, the solution to the equation is x ≈ -0.089.