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*

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

b

step-by-step explanation: