Question

A)0.8(x-3)-3.2<0.3(2-х), 0.2(1+2x)>-(x-1.6) b) 2x-1/6+x+2/3-x-8/2>x-1. 2-2x>0.5+0.5x решите систему неравенств

Answer 1

А)
1. х<5 7/11
2. х>1

Answer 2

To solve the system of inequalities, let's handle each inequality separately and then find the common solution that satisfies all of them.

a) Solving the inequalities one by one:

1. 0.8(x-3) - 3.2 < 0.3(2-x)

First, distribute the coefficients:

0.8x - 2.4 - 3.2 < 0.6 - 0.3x

Now, combine like terms:

0.8x - 5.6 < 0.6 - 0.3x

Next, move the variables to one side and constants to the other side:

0.8x + 0.3x < 0.6 + 5.6

1.1x < 6.2

Finally, divide by the coefficient of x, 1.1:

x < 6.2 / 1.1

x < 5.63636... (rounded to a reasonable decimal place)

2. 0.2(1+2x) > -(x-1.6)

First, distribute the coefficient:

0.2 + 0.4x > -x + 1.6

Next, move the variables to one side and constants to the other side:

0.4x + x > 1.6 - 0.2

1.4x > 1.4

Now, divide by the coefficient of x, 1.4:

x > 1

b) Solving the inequality:

2x - 1/6 + x + 2/3 - x - 8/2 > x - 1

Combine like terms:

2x + x - x > x - 1 + 1/6 - 2/3 + 8/2

2x > x + 1/6 - 2/3 + 4

Now, combine the constants:

2x > x + 1/6 - 2/3 + 12/6

2x > x + (1 - 4 + 12)/6

2x > x + 9/6

2x > x + 3/2

Next, move the variable term (x) to one side and the constant term (3/2) to the other side:

2x - x > 3/2

x > 3/2

Now, let's analyze the last inequality:

2 - 2x > 0.5 + 0.5x

Combine like terms:

-2x - 0.5x > 0.5 - 2

-2.5x > -1.5

Now, divide by the coefficient of x, -2.5:

x < -1.5 / -2.5

x < 0.6

Now, let's find the common solution that satisfies all the inequalities:

For inequality a: x < 5.63636... (rounded to a reasonable decimal place)

For inequality b: x > 3/2 (which means x > 1.5)

For the last inequality, x < 0.6

Putting it all together, the common solution is:

0.6 < x < 5.63636...

So, the solution to the system of inequalities is 0.6 < x < 5.63636... (rounded to a reasonable decimal place).