Pregunta
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\( -40>25-5 x \) and \( 2 x+4 \leq 29- \)

Ask by Harper Mitchell. in the United States
Feb 26,2025

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The solution to the first inequality is \( x > 13 \).

Solución

It looks like there are two inequalities in your message. The first one is   –40 > 25 – 5x. The second inequality, however, appears to be incomplete—it ends with “29–” and is missing the term or expression that should come after the minus sign. Could you please check and provide the complete form of the second inequality so I can help solve it? In the meantime, here’s the step‑by‑step solution for the first inequality: Step 1. Write the inequality:   –40 > 25 – 5x Step 2. Subtract 25 from both sides to isolate the term with x:   –40 – 25 > 25 – 5x – 25   –65 > –5x Step 3. Divide both sides by –5. Remember that dividing by a negative number reverses the inequality sign:   (–65)/(–5) < x    (inequality sign flips)   13 < x Which can be rewritten as:   x > 13 So, the solution for the first inequality is all real numbers x such that x > 13. Once you provide the complete form of the second inequality, I can help solve that as well.

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Beyond the Answer

To solve the first inequality \( -40 > 25 - 5x \), you can start by isolating \( x \). Subtract 25 from both sides to get \( -65 > -5x \). Dividing both sides by -5 (remember to flip the inequality sign when dividing by a negative number), gives \( x > 13 \). For the second inequality \( 2x + 4 \leq 29 \), begin by subtracting 4 from both sides, resulting in \( 2x \leq 25 \). Dividing both sides by 2 yields \( x \leq 12.5 \). Therefore, when combining these results, the solution indicates that there are no values for \( x \) that satisfy both inequalities, as \( x \) cannot be both greater than 13 and less than or equal to 12.5. Remember, always carefully check your work and the operations applied to inequalities, especially regarding direction changes when multiplying or dividing by negative numbers!

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