Question

solve for z and graph the solution.
8 > |z - 4| + 6
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Explanation:

Step1: Isolate the absolute - value expression

Subtract 6 from both sides of the inequality $8>|z - 4|+6$.
$8-6>|z - 4|+6 - 6$, which simplifies to $2>|z - 4|$ or $|z - 4|<2$.

Step2: Rewrite the absolute - value inequality as a compound inequality

If $|x|0$), then $-a

Step3: Solve the compound inequality for z

Add 4 to all parts of the compound inequality: $-2 + 4This gives $2

Answer:

The solution of the inequality is $2