MATH SOLVE

2 months ago

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

Accepted Solution

A:

Answer: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 side6x - 5 < 7x + 4-5 - 4 < 7x - 6x -9 < xTherefore x >-9, in set notation this would be (-9, +∞)b) x² + 3(x - 1) ≥ x² + 5We need to solve first the parentheses and combine like terms x² + 3(x - 1) ≥ x² + 5x² +3x -3 ≥ x² + 5x² - x² + 3x ≥ 5 + 33x ≥ 8 x ≥ 8/3Therefore, the solution in set notation would be [8/3, +∞)*Both graphs on the number line are below*