Question

1)|5x – 2<8;4)|3 - 4x<3​

Answer 1

1) 5x-2<8

5x<8+2

5x<10

x<2

2) 3-4x<3

-4x<0

x>0

Answer 2

Let's solve these two inequalities one by one:

1. 5x - 2 < 8

To solve this inequality, we'll isolate the variable x:

Add 2 to both sides:

5x - 2 + 2 < 8 + 2

5x < 10

Now, divide both sides by 5 (since 5 is a positive number, we don't need to reverse the inequality sign):

(5x)/5 < 10/5

x < 2

So the solution to the first inequality is x < 2.

2. 3 - 4x < 3

To solve this inequality, we'll isolate the variable x:

Subtract 3 from both sides:

3 - 4x - 3 < 3 - 3

-4x < 0

Now, divide both sides by -4. When dividing by a negative number, remember to reverse the inequality sign:

(-4x)/(-4) > 0/(-4)

x > 0

So the solution to the second inequality is x > 0.

In summary:

1. The solution to 5x - 2 < 8 is x < 2.
2. The solution to 3 - 4x < 3 is x > 0.