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2. Solve \( -\frac{1}{8} y \leq 34 \). Then graph the solution.

Ask by Bowers Chadwick. in the United States
Feb 25,2025

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Answer

The solution to the inequality \( -\frac{1}{8} y \leq 34 \) is \( y \geq -272 \). On a number line, this is represented by a closed circle at -272 and shading to the right, indicating all numbers greater than or equal to -272.

Solution

We start with the inequality:   –(1/8)y ≤ 34 Step 1: Multiply both sides by –8. Remember, when you multiply or divide an inequality by a negative number, the inequality sign reverses.   Multiplying both sides:     y ≥ 34 × (–8) Step 2: Calculate 34 × (–8):   34 × (–8) = –272, so the inequality becomes:   y ≥ –272 Thus, the solution is all y such that y is greater than or equal to –272. In interval notation, this is written as:   [–272, ∞) Graph on a number line:   • Draw a horizontal line and mark the point –272.   • Draw a closed (filled) circle at –272 to indicate that –272 is included in the solution.   • Shade or draw an arrow to the right of –272 to represent all numbers greater than –272. This completes the solution and its graph.

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Mind Expander

To solve the inequality \( -\frac{1}{8} y \leq 34 \), we start by multiplying both sides by -8. Remember, when you multiply or divide by a negative number, you must flip the inequality sign! This gives us \( y \geq -272 \). Now, to graph the solution, you would draw a number line and place a closed circle on -272 to indicate that -272 is included in the solution (since it is "greater than or equal to"). Then, shade the entire line to the right of -272, illustrating that any value greater than or equal to -272 is a solution to the inequality. Keep in mind that using the closed circle means the endpoint is included, and the shading to the right signifies all greater values are valid!

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Algebra Mexico Feb 26, 2025
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