Question

(2X-(x-4) <6 (x>3(2x-1) + 18

Answer 1

Ответ:

2x-x+4<6

x+4<6

x<2

x>6x-3+18

x>6x+15

6x<x-15

5x<-15

x<-3

Answer 2

To solve the inequality (2x - (x - 4)) < 6 and (x > 3(2x - 1) + 18), you can work through it step by step. Let's start with the first inequality:

(2x - (x - 4)) < 6

First, simplify the expression inside the parentheses:

2x - x + 4 < 6

Now, combine like terms:

x + 4 < 6

Subtract 4 from both sides:

x < 6 - 4

x < 2

Now, let's move on to the second inequality:

(x > 3(2x - 1) + 18)

First, distribute the 3 on the right side:

x > 6x - 3 + 18

Combine like terms:

x > 6x + 15

Now, subtract 6x from both sides:

x - 6x > 15

-5x > 15

To isolate x, divide both sides by -5. Remember to reverse the inequality since you're dividing by a negative number:

x < 15 / -5

x < -3

So, you have two inequalities:

1. x < 2
2. x < -3

Now, let's consider both inequalities together. Since x must satisfy both inequalities:

To satisfy both inequalities, x must be less than 2 (from the first inequality) and less than -3 (from the second inequality). Since -3 is less than 2, the only common solution is x < -3.

So, the solution to the system of inequalities is:

x < -3