Solve the inequality $0>-3x-2x$
A) $x>-36$
B) $x>-28$
C) $x>0$
D) $x>1$
Answer (1)
Combine like terms: -5x"> 0 > − 5 x .
Divide both sides by -5 (and flip the inequality sign): 0 < x .
Simplify: 0"> x > 0 .
The solution to the inequality is 0}"> x > 0 .
Explanation
Understanding the Inequality We are given the inequality -3x - 2x"> 0 > − 3 x − 2 x . Our goal is to isolate x on one side of the inequality to find the solution set.
Combining Like Terms First, we combine the like terms on the right side of the inequality: -3x - 2x"> 0 > − 3 x − 2 x
(-3 - 2)x"> 0 > ( − 3 − 2 ) x
-5x"> 0 > − 5 x
Dividing by a Negative Number Now, we want to isolate x . To do this, we divide both sides of the inequality by − 5 . Remember that when we divide or multiply an inequality by a negative number, we must flip the direction of the inequality sign: − 5 0 < − 5 − 5 x
0 < x
Solution Thus, the solution to the inequality is 0"> x > 0 .
Examples
Imagine you're managing a lemonade stand and want to ensure your profits are always positive. If your profit equation is similar to the inequality we solved, where 'x' represents the number of cups of lemonade you sell, solving the inequality helps you determine how many cups you need to sell to keep your profits above zero. This ensures your business remains viable and successful. Inequalities like these are fundamental in business for setting targets and making informed decisions about sales and costs.
