1/3(2x-1) < 5
Understand the Problem
The question is asking us to solve the inequality 1/3(2x-1) < 5 for the variable x. This will involve isolating x on one side of the inequality to find 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
- Distributing the Fraction
Start by distributing the $ \frac{1}{3} $ across the expression $ (2x - 1) $.
$$ \frac{1}{3}(2x - 1) < 5 $$
This gives us:
$$ \frac{2x}{3} - \frac{1}{3} < 5 $$
- Isolating the Fractional Term
Next, add $ \frac{1}{3} $ to both sides of the inequality to isolate the term with $ x $.
$$ \frac{2x}{3} < 5 + \frac{1}{3} $$
To add the numbers on the right, convert 5 into a fraction:
$$ 5 = \frac{15}{3} $$
Now we can combine:
$$ \frac{2x}{3} < \frac{15}{3} + \frac{1}{3} = \frac{16}{3} $$
- Clearing the Fraction
Now, multiply both sides of the inequality by $ 3 $ to eliminate the fraction.
$$ 2x < 16 $$
- Solving for x
Finally, divide both sides by $ 2 $ to solve for $ x $.
$$ x < 8 $$
The solution to the inequality is $ x < 8 $.
More Information
This inequality tells us that any number less than 8 will satisfy the inequality, which means there is an infinite range of solutions. It is commonly found in algebra when working with inequalities.
Tips
A common mistake is to forget to reverse the direction of the inequality when multiplying or dividing by a negative number. However, in this example, we did not deal with negative numbers.
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