Question

solve the absolute value inequality and graph the solution on the real number line. |2x-3|greater than or equal to 5

Answer 1

for absolute value , you need to squared the inequation
|2x-3|≥5
4x^2 -12x+9≥25
4x^2 -12x-16≥0
divide all by 4 ->
x^2 -3x-4≥0
(x-4)(x+1) ≥ 0
x = 4 x=-1
x ≤ -1 or x ≥ 4

Answer 2

oh no do not square anything.

\[|x|\geq p\] means
\[x\geq p\] or \[x\leq -p\] so solve
\[2x-3\geq5\]
\[2x\geq 8\]
\[x\geq4\]
or
\[2x-3 \leq-5\]
\[2x \leq-2\]
\[x\leq-1\]