Solve the inequality $3 x>5 x+8$
Answer (2)
x < − 4
Explanation
Understanding the Inequality We are given the inequality 5x + 8"> 3 x > 5 x + 8 and our goal is to find all values of x that make this statement true.
Isolating x Terms To solve for x , we first want to isolate the terms with x on one side of the inequality. We can subtract 5 x from both sides: 5x + 8 - 5x"> 3 x − 5 x > 5 x + 8 − 5 x This simplifies to: 8"> − 2 x > 8
Dividing by a Negative Number Now, we need to get x by itself. To do this, we divide both sides of the inequality by − 2 . It's very important to remember that when we divide (or multiply) an inequality by a negative number, we must reverse the direction of the inequality sign: − 2 − 2 x < − 2 8
Finding the Solution Simplifying the inequality, we get: x < − 4
Examples
Understanding inequalities is crucial in many real-world scenarios. For example, imagine you're managing a budget and need to ensure your expenses ( x ) stay below a certain limit (say, 1000 ) . T h e in e q u a l i t y x < 1000$ helps you determine how much you can spend without exceeding your budget. Similarly, in physics, inequalities are used to define ranges of values for variables like temperature or speed. In business, they help in setting price ranges to maximize profit while staying competitive. Inequalities are a fundamental tool for making informed decisions and setting boundaries in various aspects of life.
The solution to the inequality 5x + 8"> 3 x > 5 x + 8 is x < − 4 . To solve it, we isolate x and remember to flip the inequality sign when dividing by a negative number. Thus, the final answer is x < − 4 .
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