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select all the values \( 10 p-8 \geq 12 \) -1 0 0

Ask by Hampton Guerrero. in the United States
Feb 03,2025

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Tutor-Verified Answer

Answer

None of the values -1, 0, or 0 satisfy the inequality \( 10p - 8 \geq 12 \).

Solution

To solve the inequality \( 10p - 8 \geq 12 \), we will follow these steps: 1. **Isolate the variable \( p \)**: - Start by adding 8 to both sides of the inequality: \[ 10p - 8 + 8 \geq 12 + 8 \] This simplifies to: \[ 10p \geq 20 \] 2. **Divide both sides by 10**: - To isolate \( p \), divide both sides by 10: \[ p \geq \frac{20}{10} \] This simplifies to: \[ p \geq 2 \] Now we have determined that \( p \) must be greater than or equal to 2. Next, we will check the provided values: -1, 0, and 0. - For \( p = -1 \): \[ -1 < 2 \quad \text{(not valid)} \] - For \( p = 0 \): \[ 0 < 2 \quad \text{(not valid)} \] - For \( p = 0 \) again: \[ 0 < 2 \quad \text{(not valid)} \] None of the provided values satisfy the inequality \( p \geq 2 \). Thus, the answer is that none of the values -1, 0, or 0 are valid solutions for the inequality \( 10p - 8 \geq 12 \).

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Beyond the Answer

To solve the inequality \( 10p - 8 \geq 12 \), we first add 8 to both sides: \( 10p \geq 20 \) Then, divide both sides by 10: \( p \geq 2 \) So, we are looking for values of \( p \) that are 2 or greater. Among the options provided (-1, 0, 0), none of them satisfy the inequality since -1 and 0 are both less than 2. Now you know! Next time you encounter an inequality, remember to isolate \( p \) and check your solution against the provided values. It’s like a treasure hunt for the right answers—it makes math feel like a game! And just so you’re aware, inequalities can have all sorts of applications in real-life scenarios, from determining budgets to planning events. Being able to solve them can help you stay organized and on track. Happy solving!

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