Solve the following inequalities and express the answer in interval notation.
$1 < \frac{x - 2}{2} \leq 4$

$open bracket 4 comma 10 close paren$

$open paren 4 comma 10 close bracket$

$open bracket 0 comma 6 close paren$

$open paren 0 comma 6 close bracket$

Verified step by step guidance

Start with the compound inequality given: $1 < \frac{x - 2}{2} \le 4$.

To eliminate the fraction, multiply all parts of the inequality by 2 (which is positive, so the inequality signs remain the same): $1 \times 2 < (x - 2) \le 4 \times 2$, which simplifies to $2 < x - 2 \le 8$.

Next, isolate $x$ by adding 2 to all parts of the inequality: $2 + 2 < x - 2 + 2 \le 8 + 2$, resulting in $4 < x \le 10$.

Interpret the inequality $4 < x \le 10$ in interval notation. Since $x$ is strictly greater than 4 but less than or equal to 10, the interval is $(4, 10]$.

This interval represents all values of $x$ that satisfy the original compound inequality.

3:43m

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Solve the following inequalities and express the answer in interval notation.
$1 < \frac{x - 2}{2} \leq 4$