how do I break this down?
4x-7 <-4
over
6
the 4x-7 is all over 6 (like a fraction) I thought I just multiply by 6 to get rid of the fraction?
Yes, your first step is correct. It leaves you with
4x - 7 < -24
Then add 7 to both sides.
Then divide both sides by 4.
4x < -17.
x < -17/4
To break down the given expression, you need to solve the inequality. Here's how you can simplify it step by step:
1. Start with the inequality: (4x - 7)/6 < -4
2. To get rid of the fraction, you can multiply both sides of the inequality by 6. However, when you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality. In this case, since -4 is negative, you need to flip the inequality sign. Thus, you have:
(4x - 7)/6 * 6 > -4 * 6
4x - 7 > -24
3. Next, you want to isolate the variable x. Add 7 to both sides of the inequality:
4x - 7 + 7 > -24 + 7
4x > -17
4. Finally, divide both sides of the inequality by 4 to solve for x:
(4x)/4 > (-17)/4
x > -17/4
So, the solution to the inequality (4x - 7)/6 < -4 is x > -17/4.