Pregunta
Solve the following inequality. Write the inequality in interval notation, and graph it. \[ 8 x+5 \leq-27 \] The solution set is \( \square \). (Type your answer in interval notation.)
Ask by Cruz Nunez. in the United States
Feb 27,2025
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The solution is \( x \leq -4 \) in interval notation.
Solución
Start with the inequality:
8x + 5 ≤ -27
Step 1. Subtract 5 from both sides:
8x ≤ -27 - 5
8x ≤ -32
Step 2. Divide both sides by 8:
x ≤ -32/8
x ≤ -4
In interval notation, the solution is:
(–∞, –4]
Graph:
• Draw a number line.
• Mark the point –4 with a filled-in (closed) circle.
• Shade the portion of the line to the left of –4 to indicate that all numbers less than or equal to –4 are part of the solution.
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Simplifique esta solución Mind Expander
To solve the inequality \( 8x + 5 \leq -27 \), we first isolate \( x \). Subtract 5 from both sides: \[ 8x \leq -27 - 5 \] This simplifies to: \[ 8x \leq -32 \] Now, divide both sides by 8: \[ x \leq -4 \] In interval notation, the solution set is \( (-\infty, -4] \). Now, let's graph it! On a number line, you'd place a solid dot on -4 (indicating that -4 is included) and shade to the left towards negative infinity, showing all values less than or equal to -4 are included in the solution set.
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