Question

A) 3(x-1)>2(3-x) в) 5(x-1)+7_<1-3(x+2) б) -2-3x+1_<4

Answer 1

3(x-1)>2(3-x)3х-3>6-2x
3x+2x>6+3
5x>9
x>9/5
x>1.8 в) 5(x-1)+7_<1-3(x+2)5x-5+7_<1-3x-65x+2_<-3x-5
5x+3x_<-5-2
8x_<-7
x_<-7/8
б) -2-3x+1_<4
-1-3x_<4
-3x_<4+5
-3x_<9
x_<9/(-3)
x_<-3

Answer 2

Let's solve each of the inequalities step by step:

A) 3(x-1) > 2(3-x)

First, distribute the numbers on both sides:

3x - 3 > 6 - 2x

Now, add 2x to both sides:

3x + 2x - 3 > 6

Combine like terms:

5x - 3 > 6

Now, add 3 to both sides:

5x > 6 + 3

5x > 9

Finally, divide both sides by 5:

x > 9/5

So the solution to the inequality A) is:

x > 9/5

B) 5(x-1) + 7 ≤ 1 - 3(x+2)

First, distribute the numbers on both sides:

5x - 5 + 7 ≤ 1 - 3x - 6

Combine like terms:

5x + 2 ≤ -3x - 5

Now, add 3x to both sides:

5x + 3x + 2 ≤ -5

Combine like terms again:

8x + 2 ≤ -5

Now, subtract 2 from both sides:

8x ≤ -5 - 2

8x ≤ -7

Finally, divide both sides by 8:

x ≤ -7/8

So the solution to the inequality B) is:

x ≤ -7/8

C) -2 - 3x + 1 < 4

First, simplify the left side:

-2 - 3x + 1 < 4

-1 - 3x < 4

Now, add 1 to both sides:

-3x < 4 + 1

-3x < 5

Finally, divide both sides by -3. Remember to reverse the inequality since you're dividing by a negative number:

x > -5/3

So the solution to the inequality C) is:

x > -5/3