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

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

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Solve advanced linear inequalities

Full solution

Q.

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

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

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