Graph the solution to this inequality on the number line.
[tex]0.3(x-4) \textgreater -0.3[/tex]
Answer (2)
Divide both sides of the inequality by 0.3 : -1"> x − 4 > − 1 .
Add 4 to both sides: 3"> x > 3 .
Represent the solution on a number line with an open circle at 3 and a line extending to the right.
The solution to the inequality is 3}"> x > 3 .
Explanation
Understanding the Problem We are given the inequality -0.3"> 0.3 ( x − 4 ) > − 0.3 . Our goal is to solve for x and represent the solution on a number line. The number line will show all values of x that satisfy the inequality.
Dividing Both Sides To solve the inequality, we first divide both sides by 0.3 . Since 0.3 is a positive number, the direction of the inequality remains the same: \frac{-0.3}{0.3}"> 0.3 0.3 ( x − 4 ) > 0.3 − 0.3 -1"> x − 4 > − 1
Adding to Both Sides Next, we add 4 to both sides of the inequality to isolate x :
-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 any value of x greater than 3 will satisfy the original inequality. To represent this on a number line, we draw an open circle at 3 to indicate that 3 is not included in the solution, and then we draw a line extending to the right from 3 to indicate that all values greater than 3 are included in the solution.
Examples
Imagine you're setting up a lemonade stand and want to make a profit. If each cup of lemonade costs you 0.3 to make, and you want to ensure that after selling x cups, your profit (revenue minus cost) is greater than -$0.3 (meaning you're not losing too much money), the inequality -0.3"> 0.3 ( x − 4 ) > − 0.3 can help you determine how many cups you need to sell. Solving this inequality tells you that you need to sell more than 3 cups to meet your profit goal. This kind of problem helps in making informed decisions about sales targets and cost management in small businesses.
To solve the inequality -0.3"> 0.3 ( x − 4 ) > − 0.3 , we first simplify it to find that 3"> x > 3 . The solution can be graphically represented on a number line with an open circle at 3, extending to the right. Thus, any value greater than 3 satisfies the inequality.
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