Solve the following inequality:
[tex]9.3+x<4.4 x-(-x-6)[/tex]
Answer (2)
Simplify the inequality by distributing and combining like terms: 9.3 + x < 5.4 x + 6 .
Isolate the x terms by subtracting x and 6 from both sides: 3.3 < 4.4 x .
Divide both sides by 4.4 to solve for x : 4.4 3.3 < x .
Simplify the fraction to find the solution: 0.75"> x > 0.75 , which means x is any number greater than 0.75 . 0.75}"> x > 0.75
Explanation
Understanding the Problem We are given the inequality 9.3 + x < 4.4 x − ( − x − 6 ) . Our goal is to solve for x , which means we want to isolate x on one side of the inequality.
Simplifying the Inequality First, we simplify the right side of the inequality by distributing the negative sign: 9.3 + x < 4.4 x + x + 6 .
Combining Like Terms Next, we combine like terms on the right side: 9.3 + x < 5.4 x + 6 .
Isolating x Now, we subtract x from both sides of the inequality: 9.3 < 4.4 x + 6 .
Further Isolating x Subtract 6 from both sides: 3.3 < 4.4 x .
Dividing to Solve for x Divide both sides by 4.4: 4.4 3.3 < x .
Simplifying the Fraction Simplify the fraction: 4.4 3.3 = 44 33 = 4 3 = 0.75 . Therefore, 0.75 < x .
Final Answer The solution to the inequality is 0.75"> x > 0.75 . In interval notation, this is ( 0.75 , ∞ ) .
Examples
Imagine you're comparing phone plans. Plan A costs $9.30 plus $1 per gigabyte of data. Plan B has a fixed cost component that simplifies to $6 plus $5.40 per gigabyte. Solving the inequality helps you determine how many gigabytes you need to use for Plan A to be cheaper than Plan B. This type of problem is useful in many real-world scenarios where you need to compare costs or values based on different variables.
To solve the inequality 9.3 + x < 4.4 x − ( − x − 6 ) , we simplify to find that the solution is 0.75"> x > 0.75 . This means any value greater than 0.75 will satisfy the inequality. Thus, the final solution is represented in interval notation as ( 0.75 , ∞ ) .
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