Question
Solve the inequality \( x+3<8 \). Then graph the selutions.
Ask by Mann Cross. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the inequality \(x+3<8\) is \(x<5\). To graph this, draw a line at \(x=5\) and shade the area to the left of the line.
Solution
Solve the equation \( x+3<8 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(x+3<8\)
- step1: Move the constant to the right side:
\(x<8-3\)
- step2: Subtract the numbers:
\(x<5\)
The solution to the inequality \(x+3<8\) is \(x<5\).
To graph the solutions, we need to plot the line \(x=5\) on the number line and shade the region to the left of the line, as the inequality is less than.
The graph of the solution to the inequality \(x+3<8\) is a line at \(x=5\) with the region to the left of the line shaded.
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Simplify this solution Extra Insights
To solve the inequality \( x + 3 < 8 \), we start by isolating \( x \). Subtract 3 from both sides: \[ x < 8 - 3 \] This simplifies to: \[ x < 5 \] Now, for graphing the solutions, you would draw a number line and place an open dot at 5, indicating that 5 is not included in the solution. Then, shade all the values to the left of 5 to show that all numbers less than 5 satisfy the inequality. Now you’ve got the solution and the visual representation all set! 🎉
