Final answer:
To solve the given rational inequality, multiply both sides by the denominator to eliminate the fraction, simplify the expression, find the critical values, test the intervals, and write the final solution.
Step-by-step explanation:
To solve the rational inequality (6x+4)/(4x-1)<=3, we need to follow these steps:
- Multiply both sides of the inequality by the denominator 4x-1 to eliminate the fraction.
- Simplify the resulting expression by distributing and combining like terms.
- Move all terms to one side of the inequality to set it equal to zero.
- Factorize if possible.
- Find the critical values by setting the factors equal to zero and solving for x.
- Test the intervals using test points to see which intervals make the inequality true.
- Write the final solution by combining the intervals that satisfy the inequality.
The solution to the given rational inequality is the set of all x values that make the inequality statement true.