What is a correct first step in simplifying the expression:
-12 + 20x - 6x + 9
Answer (1)
Analyze the given expression and identify the inequality: -4x + 9"> − 12 − 2 x > − 4 x + 9 .
Add 4 x to both sides: 9"> − 12 + 2 x > 9 .
Add 12 to both sides: 21"> 2 x > 21 .
Divide both sides by 2 : \frac{21}{2}"> x > 2 21 .
Explanation
Analyzing the Expression The given expression is a combination of several expressions and an inequality, all jumbled together with typos. The first step is to try and separate these and identify what the actual problem is supposed to be. Let's rewrite the parts, correcting the typos as we go:
- 0-50-417 can be interpreted as -50 - 417 = -467
-12-20 x 5-6 x+9 can be interpreted as -12 - 20*x*5 - 6*x + 9 = -12 - 100x - 6x + 9 = -106x - 3
-12 -2 x>-4 x+9 can be interpreted as -12 - 2x > -4x + 9
-12+20 x-6 x+9 can be interpreted as -12 + 20x - 6x + 9 = 14x - 3
-12+20 x z-6 x+9 This expression contains 'z' which is not defined. Assuming it is a typo and should be '+', then it is the same as expression 4: -12 + 20x - 6x + 9 = 14x - 3
Based on these interpretations, it seems the most likely problem is to solve the inequality -12 - 2x > -4x + 9 .
Adding 4x to Both Sides To solve the inequality -12 - 2x > -4x + 9 , we need to isolate the variable x on one side of the inequality. First, add 4x to both sides: -4x + 9 + 4x"> − 12 − 2 x + 4 x > − 4 x + 9 + 4 x
9"> − 12 + 2 x > 9
Adding 12 to Both Sides Next, add 12 to both sides of the inequality: 9 + 12"> − 12 + 2 x + 12 > 9 + 12 21"> 2 x > 21
Dividing by 2 Finally, divide both sides by 2 :
\frac{21}{2}"> 2 2 x > 2 21 \frac{21}{2}"> x > 2 21 10.5"> x > 10.5
Conclusion Therefore, the first correct step in solving the inequality is to add 4x to both sides of the inequality: -12 - 2x > -4x + 9 becomes -12 + 2x > 9 .
Examples
Solving inequalities is a fundamental concept in mathematics with numerous real-world applications. For instance, consider a scenario where you want to determine the minimum number of hours you need to work to earn a certain amount of money. If you earn $15 per hour and need to make at least $300, you can set up an inequality: 15 h ≥ 300 , where 'h' represents the number of hours. Solving this inequality will tell you the minimum number of hours you need to work. Similarly, inequalities are used in various fields like economics, engineering, and computer science to model constraints and optimize solutions.
