Solve 4(2x-3) < 3x+6
Would the solution be x > 18/5?
* Algebra - Reiny, Tuesday, October 13, 2009 at 5:30pm
yes again!
Hold on... Looking back on this problem, wouldn't it be x < 18/5 since you need to flip the sign when you divide by a negative?
yes, of course, how careless of me not to notice that you switched the sign.
the correct answer is
x < 18/5
BUT, why do you think we divided by a negative?
4(2x-3) < 3x+6
8x - 12 < 3x + 6
5x < 18
x < 18/5
I decided to be different and subtract the 6 first. That lead me to divide by a negative 5 later in the equation.
You subtracted the 3x first, so you didn't have to divide by a negative at all.
Either way, the sign should be <.
You are correct, when you multiply or divide an inequality by a negative number, you need to flip the inequality sign. Let's solve the inequality step by step to confirm the correct solution.
Given inequality: 4(2x-3) < 3x+6
Step 1: Distribute on the left side
8x - 12 < 3x + 6
Step 2: Move all the x terms to one side and the constant terms to the other side
8x - 3x < 6 + 12
Step 3: Simplify both sides of the inequality
5x < 18
Step 4: Divide both sides of the inequality by 5
x < 18/5
So, you are correct. The solution to the inequality is x < 18/5, not x > 18/5.