Kendall is solving this inequality:
[tex]x / 2+6\ \textgreater \ 42[/tex]
What should she do first to solve?
A. Subtract 6 from both sides of the inequality.
B. Divide both sides of the inequality by 2.
C. Add 6 to both sides of the inequality.
D. Add 42 to both sides of the inequality.
Answer (1)
Subtract 6 from both sides of the inequality to isolate the term with x: 42 - 6"> x /2 + 6 − 6 > 42 − 6 .
Simplify the inequality: 36"> x /2 > 36 .
The first step is to subtract 6 from both sides.
Therefore, the correct first step is to subtract 6 from both sides of the inequality.
Explanation
Analyze the Inequality The problem is to determine the first step in solving the inequality 42"> x /2 + 6 > 42 . To isolate x , we need to undo the operations that are applied to it in reverse order. The operations applied to x are division by 2 and addition of 6. Therefore, we should first subtract 6 from both sides of the inequality.
Subtract 6 from both sides Subtracting 6 from both sides of the inequality gives us: 42 - 6"> x /2 + 6 − 6 > 42 − 6 36"> x /2 > 36
Conclusion The first step to solve the inequality is to subtract 6 from both sides of the inequality.
Examples
When solving real-world problems, like determining how many items you need to sell to make a certain profit, you often need to solve inequalities. For example, if each item sells for $2 and you have fixed costs of $6, the inequality 42"> 2 x + 6 > 42 can help you find the number of items, x , you need to sell to make a profit greater than $42. The first step is to subtract the fixed costs from both sides to isolate the variable term.
