Answer:
a) (-9, +∞)
b) [8/3, +∞)
Explanation:
a) 6x - 5 < 7x + 4
We need to write the terms with x on one side and the terms without x on the other side
6x - 5 < 7x + 4
-5 - 4 < 7x - 6x
-9 < x
Therefore x >-9, in set notation this would be (-9, +∞)
b) x² + 3(x - 1) ≥ x² + 5
We need to solve first the parentheses and combine like terms
x² + 3(x - 1) ≥ x² + 5
x² +3x -3 ≥ x² + 5
x² - x² + 3x ≥ 5 + 3
3x ≥ 8
x ≥ 8/3
Therefore, the solution in set notation would be [8/3, +∞)
*Both graphs on the number line are below*