Solve the inequality and express the solution in terms of intervals:

x-2/3x+5 ≤ 4
This is how I did it:
x-2/3x+5 - 4(3x+5) ≤ 0
x-2-12x-20/3x+5 ≤ 0
-11(x+2)/3x+5 ≤ 0
Can you please tell me if the answer is right and if so then how do we express the solution in terms of interval?
Like this? (-5/3, -2) ?

math is ok, but intervals have the smaller value first.

Also, you have a closed interval, since it's ≤ and not <. So your interval is

[-2,-5/3]

Your steps for solving the inequality are correct up to this point:

-11(x+2)/3x+5 ≤ 0

To express the solution in terms of intervals, we need to find the values of x that make the expression less than or equal to zero.

First, let's find the critical points, which are the values of x where the numerator (x+2) and the denominator (3x+5) become zero.

Numerator:
x + 2 = 0
x = -2

Denominator:
3x + 5 = 0
3x = -5
x = -5/3

Now we have three intervals to consider: (-∞, -5/3), (-5/3, -2), and (-2, +∞).

To determine whether the expression is less than or equal to zero within each interval, we can choose test points. A convenient test point in each interval is the midpoint of the interval.

For (-∞, -5/3), we can choose x = -2 as the test point.
-11(-2+2)/(3(-2)+5) ≤ 0
0/(-6+5) ≤ 0
0/-1 ≤ 0
0 ≤ 0
The expression is true, so this interval is part of the solution.

For (-5/3, -2), we can choose x = -1 as the test point.
-11(-1+2)/(3(-1)+5) ≤ 0
-11/(-3+5) ≤ 0
-11/2 ≤ 0
The expression is false, so this interval is not part of the solution.

For (-2, +∞), we can choose x = 0 as the test point.
-11(0+2)/(3(0)+5) ≤ 0
-11/5 ≤ 0
The expression is true, so this interval is part of the solution.

Putting it all together, the solution to the inequality is (-∞, -5/3] ∪ (-2, +∞).