If an inequality is y is greater than or equal to 10 - x, how do I make 10 switch places with x?
Understand the Problem
The question is asking how to rearrange the inequality y ≥ 10 - x to isolate x on one side. This involves manipulating the inequality by adding or subtracting terms appropriately.
Answer
The rearranged inequality is $x \geq 10 - y$.
Answer for screen readers
The rearranged inequality is
$$ x \geq 10 - y $$
Steps to Solve
- Start with the original inequality
The original inequality is
$$ y \geq 10 - x $$
- Isolate the term with x
To isolate the x term on one side, we can add x to both sides of the inequality:
$$ y + x \geq 10 $$
- Rearrange to isolate x
Next, subtract y from both sides to isolate x:
$$ x \geq 10 - y $$
Now, we have isolated x on one side of the inequality.
The rearranged inequality is
$$ x \geq 10 - y $$
More Information
This rearrangement allows us to express x in terms of y, which can be useful for graphing the inequality or solving related problems. The graph of this inequality will show the area above the line defined by $x = 10 - y$.
Tips
- Not changing the direction of the inequality: When multiplying or dividing by a negative number, the direction of the inequality must change. However, this problem solely involves addition and subtraction, so be careful to remember that.
- Forgetting to keep the inequality symbol: When manipulating inequalities, some may forget to carry the inequality symbol through each step.
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