Final answer:
To find the solution set for the inequality 2-3x<3(6-5x), distribute the 3, collect like terms, isolate the variable x, and solve, making sure to reverse the inequality when dividing by a negative number. The solution set is x > 4/3 or x > 1.33.
Step-by-step explanation:
To determine the solution set for the inequality 2-3x<3(6-5x), follow these steps:
- Simplify the inequality by distributing the 3 across the terms within the parentheses on the right-hand side: 2 - 3x < 18 - 15x.
- Next, get all the 'x' terms on one side by adding 3x to both sides: 2 < 18 - 12x.
- Then, to isolate 'x', subtract 18 from both sides: -16 < -12x.
- To solve for 'x', divide both sides by -12. Remember to reverse the inequality when you divide by a negative number: x > 16/12.
- Simplify the fraction to get the solution set: x > 4/3 or in decimal form, it's x > 1.33.
Think about your result to make sure it makes sense. Since we have divided by a negative number, we made sure to reverse the inequality sign.