How do you graph and solve $∣ ∣ 2 - \frac{x}{2} ∣ ∣ - 1 \leq 1$ $abs[2-x/2]-1<=1$ ?

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Answer 1 · 2018-05-16T09:24:40

$0 \leq x \leq 8$ $0<=x<=8$ or $x \in [0, 8]$ $x in[0,8]$

Add one to both sides to get:
$∣ ∣ 2 - \frac{x}{2} ∣ ∣ \leq 1$ $abs(2-x/2)<=1$

Now since we have $| |$ $abs()$ we ca take the positive or negative of the function:

$2 - \frac{x}{2} \leq 2$ $2-x/2<=2$
$- \frac{x}{2} \leq 0$ $-x/2<=0$
$- x \leq 0$ $-x<=0$
$x \geq 0$ $x>=0$

or

$\frac{x}{2} - 2 \leq 2$ $x/2-2<=2$
$\frac{x}{2} \leq 4$ $x/2<=4$
$x \leq 8$ $x<=8$

Combining these gives us:
$0 \leq x \leq 8$ $0<=x<=8$ or $x \in [0, 8]$ $x in[0,8]$

How do you graph and solve abs[2-x/2]-1<=1∣∣2−x2∣∣−1≤1 abs[2-x/2]-1<=1?