42y-36>6(6y-13) solve using multiplication principle??

Question

The answer is [-7, infinity] Can you break down how to get this answer Thanks

Answer 1

multiply both sides by 1/6 and get
7y - 6 > 6y - 13
y > -7
which in interval notation is (-7,∞) using (), not []. [] denote a closed interval. y ≥ -7 would be [-7,∞).

Answer 2

42y-36>6(6y-13)
get y by itself
42y-36>36y-78
6y>-42
y>-7

in order for this to be true y can be any number >-7
depending on what math your in the real answer is (-7,infinity), not
[-7,infinity) but just a technicality

Answer 3

"Multiplication Principle"? Do you mean the distributive property of multiplication over addition? a(b+c)=ab+ac?
The right side is
6(6y-13) Using the distributive property,
= (6)(6y) - (6)(13)... doing the arithmetic.
= 36y - 78

So the problem is now
42y-36>36y-78

Add 36 to both sides
42y >36y - 42

Add -36y to both sides
6y > -42

Multiply both sides by 1/6
y > -7,,, your solution set

Set theoretically (-7, ∞)... square brackets [-7, and ∞] mean that the values are included. -7 is not included, and ∞ is not a value to be included.

Answer 4

42y-36>6(6y-13)
42y-36>36y-78
6y>-42
y>-7
hence the range is -7 to infinity