Find the solution set to each inequality. express the solution in set notation and graphically on the number line.
a. 6x - 5 < 7x + 4
b. x² + 3(x - 1) ≥ x² + 5

a) (-9, +∞)

b) [8/3, +∞)

Step-by-step 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*