Solve the inequality in set notation or interval notation

Question

-6<2-4x< 27

Answer 1

Hi Jackie,

To solve this, you would split the inequality into the two halves and solve for x separately.

First, let's solve -6≤2-4x

1. Subtract 2 from both sides
2. (-6-2)≤-4x
3. -8≤-4x
4. Divide both sides by -4 (note that dividing by a negative number flips the inequality sign)
5. (-8/-4)≥(-4x/-4)
6. 2≥x

Next, let's solve 2-4x≤27

1. Subtract 2 from both sides
2. -4x≤25
3. Divide both sides by -4
4. -25/4≤x

Now, combine the two inequalities: -25/4≤x≤2

In interval notation, this would be [-25/4,2] with the square brackets indicating inclusion of the endpoints.

In set notation, this would be {x|-25/4≤x≤2} meaning the set includes all x greater than or equal to -25/4, and less than or equal to 2