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Solve each compound inequality.
3 <= 2x-1 <= 11
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Solve each compound inequality. $3 \leq 2 x-1 \leq 11$ $\newline$ Upload $\newline$ Choose a File

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Estimate products of mixed numbers

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Q. Solve each compound inequality.

3 \leq 2 x-1 \leq 11

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Split and Solve First Inequality: First, we need to solve the compound inequality $3 \leq 2x - 1 \leq 11$ by splitting it into two separate inequalities and solving each one. $\newline$ The first inequality is $3 \leq 2x - 1$ . $\newline$ We will add $1$ to both sides of the inequality to isolate the term with the variable $x$ . $\newline$ $3 + 1 \leq 2x - 1 + 1$ $\newline$ $4 \leq 2x$
Solve for x: Now, we divide both sides of the inequality by $2$ to solve for $x$ . $\newline$ $\frac{4}{2} \leq \frac{2x}{2}$ $\newline$ $2 \leq x$
Split and Solve Second Inequality: The second part of the compound inequality is $2x - 1 \leq 11$ . We will add $1$ to both sides of this inequality as well. $2x - 1 + 1 \leq 11 + 1$ $2x \leq 12$
Solve for x: We divide both sides of this inequality by $2$ to solve for x. $\newline$ $\frac{2x}{2} \leq \frac{12}{2}$ $\newline$ $x \leq 6$
Combine and Find Solution Set: Now we combine the results from both inequalities to find the solution set for the compound inequality. $\newline$ From the first part, we have $x \geq 2$ , and from the second part, we have $x \leq 6$ . $\newline$ Therefore, the solution set is all $x$ values between $2$ and $6$ , inclusive.

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