1/3(2x - 1) < 5
Understand the Problem
The question is asking to solve the inequality (1/3)(2x - 1) < 5 for the variable x. We will approach this by isolating x and determining the range of values that satisfy the inequality.
Answer
$x < 8$
Answer for screen readers
The solution to the inequality is $x < 8$.
Steps to Solve
- Multiply by 3 to eliminate the fraction
To remove the fraction in the inequality, multiply both sides by 3:
$$ 3 \cdot \left(\frac{1}{3}(2x - 1)\right) < 3 \cdot 5 $$
This simplifies to:
$$ 2x - 1 < 15 $$
- Add 1 to both sides
Next, we want to isolate the term with $x$. To do this, add 1 to both sides of the inequality:
$$ 2x - 1 + 1 < 15 + 1 $$
This simplifies to:
$$ 2x < 16 $$
- Divide by 2 to solve for x
Now, divide both sides by 2 to find the value of $x$:
$$ \frac{2x}{2} < \frac{16}{2} $$
This simplifies to:
$$ x < 8 $$
The solution to the inequality is $x < 8$.
More Information
This result means that any value of $x$ that is less than 8 will satisfy the original inequality. For example, values such as 0, 5, or 7 will work, whereas 8 and numbers greater will not.
Tips
- Not reversing the inequality: When multiplying or dividing by a negative number, you must reverse the inequality sign. However, in this case, since all operations were by positive numbers, no reversing occurred.
- Miscalculating during steps: Be careful while adding or multiplying, as simple arithmetic mistakes can lead to incorrect conclusions.
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