1)-5 <= -3X+1 < 1

2)4X-2 < 6 OR X+2 > 9

Please help me with this problem! I am going CRAZY!!!!!!!!!



Hi,

Let's do the second problem first. there are two inequalities and I am going to solve them separately.

4X-2 < 6 Add 2 to both sides as you would if this were an equation rather than an inequality. This gives 4X-2+2 < 6+2 or 4X < 8 Now multiply both sides by  1/4 to get  1/4(4X) <  1/4(8) or X < 2 The important point here is that if you multiply both sides of an inequality by the same positive number then the direction of the inequality remains unchanged.

For the second inequality, X+2 > 9, subtract 2 from each side to get

X > 7

Thus the answer to your second problem is

all X that satisify either X < 2 OR X > 7

The first problem is also two inequalities but you can solve both of them at the same time. First subtract 1 from both sides of each inequality.

-5 -1 <= -3X+1 -1 < 1 -1 or -6 <= -3X < 0

Now multiply both sides of each inequality by -1/3. This time, since you are multiplying by a negative quantity, the direction of the inequalities reverse.

-1/3(-6) >= -1/3(-3X) > -1/3(0) or 2 >= X > 0 which you can also write 0 < X <= 2

Cheers,
Penny

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