Solve the inequality for [tex]$x$[/tex].
[tex]$8+\frac{x}{6}>2$[/tex]
Simplify your answer as much as possible.
Answer (2)
Subtract 8 from both sides: 2 - 8"> 6 x > 2 − 8 .
Simplify: -6"> 6 x > − 6 .
Multiply both sides by 6: -6 \times 6"> x > − 6 × 6 .
The solution is: -36}"> x > − 36 .
Explanation
Understanding the Inequality We are given the inequality 2"> 8 + 6 x > 2 . Our goal is to isolate x on one side of the inequality to find the solution.
Subtracting 8 from Both Sides First, we subtract 8 from both sides of the inequality to get 2 - 8"> 6 x > 2 − 8 .
Simplifying the Inequality Simplifying the right side, we have -6"> 6 x > − 6 .
Multiplying by 6 Next, we multiply both sides of the inequality by 6 to isolate x : -6 \times 6"> x > − 6 × 6 .
Final Solution Finally, we simplify the right side to find the solution: -36"> x > − 36 . This means that x can be any number greater than -36.
Examples
Imagine you're saving money, and you have 8 a l re a d y . I f yo u s a v e ana dd i t i o na l am o u n t e a c h w ee k ( \frac{x}{6}$), this problem helps you determine how much you need to save in total (x) to have more than $2. Understanding inequalities helps in budgeting and financial planning to ensure you meet your savings goals.
To solve the inequality 2"> 8 + 6 x > 2 , we subtract 8 from both sides to get -6"> 6 x > − 6 , then multiply both sides by 6 to find -36"> x > − 36 . Thus, the solution is x greater than -36. This means that any number more than -36 satisfies the inequality.
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