Please help me with interval notation?

Question

I am trying to figure out how to solve these but, honestly, I just dont remember and I cannot figure out the right answers.

Solve the following inequality. Write the answer in interval notation.

3x+7 < 2

Solve the following inequality. Write the answer in interval notation.

5(3-x) > 3x-1

Answer 1

Inequalities are easier than what you think :)

Given

3x+7&lt; 2

=&gt;

3x&lt; 2 -7

=&gt;

3x &lt; -5

=&gt;

x &lt; -5/3       (x is smaller than -5/3 so it lies between -inf and -5/3)

Thus the interval  (your answer) for x is  (-00, -5/3)

======================================...

Similarly

5(3-x) &gt; 3x-1

=&gt;

15-5x &gt; 3x -1

=&gt;

16&gt; 8x

=&gt;

2&gt; x

Thus the answer is x ε (-00, 2)