Question
Solve the inequality and complete a line graph representing the solution. In a minimum of two sentences, describe the solution and the line graph. \( 8 \geq 3 x+5 \)
Ask by Bolton Williams. in South Africa
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution to the inequality \( 8 \geq 3x + 5 \) is \( x \leq 1 \). On the number line, this is shown by a solid dot at 1 and shading all numbers to the left, indicating that any value of \( x \) less than or equal to 1 satisfies the inequality.
Solution
To solve the inequality \( 8 \geq 3x + 5 \):
1. **Subtract 5 from both sides**:
\[
8 - 5 \geq 3x \quad \Rightarrow \quad 3 \geq 3x
\]
2. **Divide both sides by 3**:
\[
\frac{3}{3} \geq x \quad \Rightarrow \quad 1 \geq x \quad \text{or} \quad x \leq 1
\]
**Line Graph Description**:
On a number line, draw a solid circle at \( x = 1 \) to indicate that 1 is included in the solution. Shade all the numbers to the left of 1, representing all real numbers less than or equal to 1. This visual clearly shows that any value of \( x \) up to and including 1 satisfies the inequality \( 8 \geq 3x + 5 \).
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution The Deep Dive
To solve the inequality \( 8 \geq 3x + 5 \), we first subtract 5 from both sides to get \( 3 \geq 3x \). Dividing both sides by 3 gives \( 1 \geq x \), or equivalently, \( x \leq 1 \). In the line graph, you would draw a horizontal line on the number line from negative infinity up to and including 1, with a solid dot at 1 to indicate that it is included in the solution set. This indicates that all numbers less than or equal to 1 are part of the solution, visually demonstrating that this is a continuous range.
