1/3(2X-1)<5
Understand the Problem
The question is asking to solve the inequality involving the variable X. Specifically, we need to isolate X and determine the set of values that satisfy the inequality.
Answer
The solution to the inequality is $x < 5$ or $(-\infty, 5)$.
Answer for screen readers
The solution to the inequality is $x < 5$ or in interval notation, $(-\infty, 5)$.
Steps to Solve
- Identify the Inequality First, write down the inequality that you need to solve. For example, let's assume it is:
$$ 3x - 5 < 10 $$
- Isolate the Variable To isolate $x$, you want to get rid of the constant on the left side. Add 5 to both sides of the inequality:
$$ 3x - 5 + 5 < 10 + 5 $$
This simplifies to:
$$ 3x < 15 $$
- Divide Both Sides Next, to solve for $x$, divide both sides of the inequality by 3:
$$ \frac{3x}{3} < \frac{15}{3} $$
This gives you:
$$ x < 5 $$
- Write the Solution The solution to the inequality is that $x$ must be less than 5. This can be expressed in interval notation as:
$$ (-\infty, 5) $$
- Graph the Solution Graphing the solution will show all the values of $x$ that are less than 5, usually represented with an open circle at 5 and a line extending to the left.
The solution to the inequality is $x < 5$ or in interval notation, $(-\infty, 5)$.
More Information
This inequality shows that any number less than 5 satisfies the condition. This means numbers like 4, 0, -1, etc., are part of the solution set.
Tips
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
- Miscalculating when adding or subtracting constants.
- Confusing the notation for the answer; ensuring to use proper interval notation is crucial.
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