5/3x-7≤2
Solve. Note in interval notation
So I got 19/6≤x
the other is suppose to be
x less than 7/3 but I can't get that
How do you get that
5/(3x-7) <= 2
If 3x-7 > 0 (x > 7/3), then
5 <= 2(3x-7)
5/2 <= 3x-7
19/2 <= 3x
19/6 <= x
x >= 19/6
The original condition was x > 7/3, so x >= 19/6 works.
If 3x-7 < 0 (x < 7/3),
5 >= 2(3x-7)
19/6 >= x
x <= 19/6
The original condition was x < 7/3, but 7/3 < 19/6, so only the x < 7/3 part is a solution.
To solve the inequality 5/3x - 7 ≤ 2, we will follow these steps:
1. Add 7 to both sides of the inequality: 5/3x - 7 + 7 ≤ 2 + 7
This simplifies to: 5/3x ≤ 9
2. To eliminate the fraction, multiply both sides of the inequality by the reciprocal of 5/3, which is 3/5 (flipping the fraction): (3/5)(5/3)x ≤ (3/5)(9)
This simplifies to: x ≤ 27/5
So far, we have x ≤ 27/5 or x less than or equal to 5.4.
Next, let's simplify it further to get the second part of the solution.
3. To convert the decimal 5.4 into a fraction, we write it as a fraction over 1: 5.4 = 5.4/1
4. To convert this into a fraction, we multiply numerator and denominator by 10, as there is one decimal digit after the decimal point: (5.4/1) * (10/10) = 54/10
5. Simplify the fraction 54/10 by dividing the numerator and denominator by their greatest common divisor, which is 2: (54/10) ÷ 2/2 = 27/5
So, the solution to the inequality 5/3x - 7 ≤ 2 in interval notation is:
x ≤ 27/5 or x ≤ 5.4
In other words, x is less than or equal to 27/5 or 5.4.