To calculate: Thesolution of compound inequality −2≤4−x3≤6, if possible then write theanswer in interval notation.

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To calculate: Thesolution of compound inequality  −2≤4−x3≤6,  if possible then write theanswer in interval notation.

smallq9 · Accepted Answer

Step 1  Consider the compound inequality, −2≤4−x3≤6  Simplify the left and middle side of the compound inequality, −2≤4−x3≤6  −2≤4−x3  4−x3≥−2  Multiply both side by 3,  3(4−x)3≥3⋅(−2)  4−x≥−6  −x≥−10  x≤10  Simplify the right and middle side of the compound inequality, −2≤4−x3≤6  4−x3≤6  Multiply both side by 3,  3(4−x)3≤6⋅3  4−x≤18  −x≤14  x≥−14  Thus, x≤10 and x≥−14, in interval notation, it can be denoted as [−14, 10]  Hence, the solution of compound inequality −2≤4−x3≤6 is [−14, 10]

To calculate: Thesolution of compound inequality -2\leq\frac{4-x}{3}\leq6

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