Question

Solve the inequality: 6a(a − 1) − 2a(3a − 2) < 6

Answer 1

To solve the inequality 6a(a - 1) - 2a(3a - 2) < 6, expand the expression, combine like terms, solve for 'a', and remember to reverse the inequality sign when multiplying or dividing by a negative number. The solution is a > -3.

Step-by-step explanation:

To solve the inequality 6a(a − 1) − 2a(3a − 2) < 6, we start by expanding and simplifying:

1. Multiply out the brackets: 6a² - 6a - 6a² + 4a.
2. Combine like terms: -6a + 4a, which simplifies to -2a.
3. Set the inequality -2a < 6.
4. Divide both sides by -2, remembering that this reverses the inequality sign, giving us a > -3.

To check the answer and ensure it is reasonable, we can test a value greater than -3 in the original inequality.