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b. Solve: \( -3 x-24 \leq-36 \)

Ask by King Bolton. in the United States
Jan 22,2025

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Answer

\( x \geq 4 \)

Solution

To solve the inequality: \[ -3x - 24 \leq -36 \] **Step 1: Add 24 to both sides** \[ -3x - 24 + 24 \leq -36 + 24 \] \[ -3x \leq -12 \] **Step 2: Divide both sides by -3** *Remember:* When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign. \[ \frac{-3x}{-3} \geq \frac{-12}{-3} \] \[ x \geq 4 \] **Solution:** \[ x \geq 4 \]

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To solve the inequality \( -3x - 24 \leq -36 \), first, let's isolate the term involving \( x \). Start by adding \( 24 \) to both sides: \[ -3x - 24 + 24 \leq -36 + 24 \] This simplifies to: \[ -3x \leq -12 \] Now, divide both sides by \( -3 \). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign: \[ x \geq 4 \] So, the solution is \( x \geq 4 \). Now, let’s think about this inequality in real-world terms! Imagine you’re planning a party and need at least 4 friends to join you for it to be a good time. If you currently have \( x \) friends and you're thinking about inviting some more, the inequality shows that you need to ensure you have at least 4 friends willing to come over to create that lively atmosphere you desire! When solving inequalities, it's easy to make a common mistake by forgetting to flip the inequality sign when multiplying or dividing by a negative number. This can lead to incorrect solutions. Always double-check your steps, especially when dealing with negativity; it can really change the game!

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