Question

Решите неравенство: а) 6х  – 18; в) 0,5(х – 2) + 1,5х < х + 1. б) – 4х > 36;

Answer 1

1)6(х-3)
2)0,5x -1+1,5x<x+1
2x-1<x+1
2x-x<1+1
x<2
3)x<36\-4
x<-9

Answer 2

I can help you solve the inequality. Here is the detailed solution:

a) 6x ≥ -18 To solve this inequality, we need to isolate x on one side of the sign. We can do this by dividing both sides by 6, which is the coefficient of x. This gives us:

x ≥ -18/6

Simplifying the fraction, we get:

x ≥ -3

This is the solution of the inequality. It means that x can be any real number that is greater than or equal to -3. We can also write the solution in interval notation as:

[-3, +∞)

This means that x belongs to the interval from -3 to positive infinity, including -3.

b) -4x > 36 To solve this inequality, we need to isolate x on one side of the sign. We can do this by dividing both sides by -4, which is the coefficient of x. However, we need to remember that when we divide or multiply an inequality by a negative number, we have to reverse the direction of the sign. This gives us:

x < 36/(-4)

Simplifying the fraction, we get:

x < -9

This is the solution of the inequality. It means that x can be any real number that is less than -9. We can also write the solution in interval notation as:

(-∞, -9)

This means that x belongs to the interval from negative infinity to -9, not including -9.

c) 0.5(x - 2) + 1.5x < x + 1 To solve this inequality, we need to collect all the terms with x on one side of the sign, and all the constants on the other side. We can do this by expanding the brackets, subtracting x from both sides, and adding 1 to both sides. This gives us:

0.5x - 1 + 1.5x - x < 1 + 1

Simplifying the expression, we get:

x - 1 < 2

To isolate x, we need to add 1 to both sides. This gives us:

x < 2 + 1

Simplifying the expression, we get:

x < 3

This is the solution of the inequality. It means that x can be any real number that is less than 3. We can also write the solution in interval notation as:

(-∞, 3)

This means that x belongs to the interval from negative infinity to 3, not including 3.