Final answer:
The inequality -5(x-6)+3>0 is solved by distributing, combining like terms, and isolating the variable, leading to the solution set (-∞, 6.6).
Step-by-step explanation:
To solve the inequality -5(x-6)+3>0, follow these steps:
- Distribute the -5 into the parentheses: -5x + 30 + 3 > 0.
- Combine like terms: -5x + 33 > 0.
- Subtract 33 from both sides to isolate the variable term: -5x > -33.
- Divide both sides by -5, remembering to reverse the inequality since we are dividing by a negative number: x < 33/5.
- Simplify the fraction if possible, in this case, it becomes x < 6.6.
The solution set is all real numbers less than 6.6, which can also be written as (-∞, 6.6) in interval notation.