How do you solve #abs((2 - 5x)/4) >= 2/3#?

1 Answer
Apr 7, 2015

Solution

Modulus function can be removed by replacing with definition.
1.#|(2-5x)/4|>=2/3# can be solved in the following way.

2.#|(2-5x)/4|=sqrt((2-5x)^2)/sqrt(16)#
3.#=sqrt((4-10x+25x^2)/16)>=2/3#
4.#(4-10x+25x^2)/16>=4/9#
5.#25x^2-10x+4-64/9>=0#
6.#25x^2-10x-28/9>=0#
The boundary is when x satisfies the above equations. Hence
7.#x=(10+-sqrt(100+4*25*28/9))/50#
8.#x=(30+-sqrt(2900))/150#
9.#x=0.559011,-0.15901#
For the #>=# constraint to be satisfied the points have to be on the right side of the curve and the left side of the curve.Constructed Using MATLAB
The given plot is for when the equation 6 satisfies the value of zero.