1: Solve and write the solution in interval notation: ?

Question

2x - 4 < 4 or x + 5 ≤ 2 - 2x

(-∞, 3)

(-∞, 4)

(-∞, ∞)

(-1, 4)

Answer 1

Simplify each equation

For the first equation, add 4 to each side

2x &lt; 8

and divide each side by 2

x &lt; 4

For the second equation, add 2x to each side

3x + 5 &lt;= 2

and subtract 5 from each side

3x &lt;= -3

and divide by 3

x &lt;= -3

So you now have

x &lt; 4 or x&lt;= -3

A OR B means A, B or A and B must be true.  So, in this case,

any number less than 4 satisfies the OR

The answer is....

(-∞, 4)

Answer 2

(-1,4)  

Answer 3

2x &lt; 8 or 3x &lt;= -3

x &lt; 4 or x &lt;= -1

x &lt; 4

(-infinity , 4)