Question

|2x=3| is greater than or equal to 19

Answer 1

Do you mean |2x-3|≥19? One solution is 2x-3≥19, 2x≥22, x≥11.

We can also write 2x-3≤-19, 2x≤-16, x≤-8. Solution: x≥11 or x≤-8.

Here's another way (removing absolute | |):

(2x-3)²≥19²,

4x²-12x+9≥361,

4x²-12x-352≥0,

4(x²-3x-88)=4(x-11)(x+8)≥0. (NOTE: we already know that x=11 is a solution, so we would expect this factor).

For this inequality to be true: x-11≥0 and x+8≥0⇒x≥11 (because 11>-8); or x-11≤0 and x+8≤0⇒x≤-8 (because -8<11).

Solution: x≥11 or x≤-8.