(x)/(2)-5

Question

(x)/(2)-5 <= 3(x+2) < 9

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Deal with left part: First, we will deal with the left part of the compound inequality (x)/(2)-5 <= 3(x+2). Distribute the 3 on the right side of the inequality. (x)/(2)-5 <= 3x+6Isolate x: Next, we will isolate x on one side of the inequality. To do this, we will first get rid of the -5 on the left side by adding 5 to both sides. (x)/(2) <= 3x+11Multiply by 2: Now, we will multiply both sides by 2 to get rid of the fraction. x <= 6x+22Move terms with x: Next, we will move all terms containing x to one side by subtracting 6x from both sides. x - 6x <= 22Combine like terms: Combine like terms. -5x <= 22Divide by -5: Now, we will divide both sides by -5, remembering to flip the inequality sign because we are dividing by a negative number. x >= -22/5 x >= -4.4Deal with right part: Now we will deal with the right part of the compound inequality 3(x+2) < 9. Distribute the 3 on the left side of the inequality. 3x+6 < 9Isolate x: Next, we will isolate x on one side of the inequality. To do this, we will subtract 6 from both sides. 3x < 3Divide by 3: Now, we will divide both sides by 3 to solve for x. x < 1Combine both parts: Finally, we combine the two parts of the compound inequality to find the range of values for x. x >= -4.4 and x < 1

\frac{x}{2}-5 \leq 3(x+2)<9

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