Use the drawing tools to form the correct answer on the number line. Graph the solution to this inequality on the number line: [tex]$0.3(x-4)\ \textgreater \ -0.3$[/tex]
Answer (1)
Divide both sides of the inequality -0.3"> 0.3 ( x − 4 ) > − 0.3 by 0.3 to get -1"> x − 4 > − 1 .
Add 4 to both sides to isolate x , resulting in 3"> x > 3 .
Represent the solution 3"> x > 3 on a number line with an open point at 3 and a ray extending to the right.
The solution to the inequality is 3"> x > 3 , which is graphed on the number line. 3}"> x > 3
Explanation
Understanding the Problem We are given the inequality -0.3"> 0.3 ( x − 4 ) > − 0.3 and we want to find the solution and graph it on the number line.
Dividing by 0.3 To solve the inequality, we first divide both sides by 0.3 :
\frac{-0.3}{0.3}"> 0.3 0.3 ( x − 4 ) > 0.3 − 0.3 -1"> x − 4 > − 1
Adding 4 to both sides Next, we add 4 to both sides of the inequality: -1+4"> x − 4 + 4 > − 1 + 4 3"> x > 3
Graphing the Solution The solution to the inequality is 3"> x > 3 . This means that x can be any number greater than 3, but not equal to 3. To represent this on the number line, we use an open point at 3 to indicate that 3 is not included in the solution, and a ray extending to the right to indicate all values greater than 3.
Examples
Imagine you're measuring the temperature of a chemical reaction. The inequality 3"> x > 3 could represent the minimum temperature (in degrees Celsius) needed for the reaction to occur safely. Graphing this on a number line helps visualize the safe operating range, ensuring the temperature stays above the critical threshold to prevent any hazardous outcomes. This concept applies to various real-world scenarios, such as setting minimum speed limits, defining acceptable ranges for product dimensions, or determining the minimum number of participants needed for an event.
