9A. Solve the inequality.Show all steps.15 > 7 - t/3
9B. Check your work.
Hi. I'm not trying to cheat. I don't understand the equation. If you see another question by me with the same question, I'm sorry. I had hit submit and it wasn't there. Sorry.
15 > 7 - t/3
The method for solving in-equations is the same as that for solving equation, except:
when you multiply or divide by a negative number, you must reverse the inequality sign
add t/3 to both sides
t/3 + 15 > 7
subtract 15 from both sides
t/3 > -8
multiply both sides by +3, nothing happens to the > sign
t > -24
Awesome! That makes sense. Thanks!
No problem at all! I'm here to help you understand and solve the inequality equation. Let's break it down step by step.
9A. Solve the inequality: 15 > 7 - t/3
Step 1: To begin, let's isolate the variable t by getting rid of the constant term on the right side of the inequality. We can do this by subtracting 7 from both sides of the equation. This gives us:
15 - 7 > 7 - 7 - t/3
8 > -t/3
Step 2: Next, we want to get rid of the fraction -t/3. To do this, we can multiply both sides of the inequality by -3. Remember, when multiplying or dividing an inequality by a negative number, we need to reverse the inequality sign. This gives us:
8(-3) < (-t/3)(-3)
-24 < t
So the solution to the inequality is t > -24.
9B. To check our work, we can substitute a value that is greater than -24 into the original inequality and see if it holds true. Let's choose t = -20, which is greater than -24.
Original inequality: 15 > 7 - t/3
Substitute t = -20:
15 > 7 - (-20)/3
15 > 7 + 20/3
Evaluating the right side:
15 > 7 + 6.67
15 > 13.67
Since 15 is indeed greater than 13.67, the inequality holds true when t = -20. Therefore, our solution t > -24 is correct.
I hope this explanation helps you understand how to solve and check an inequality equation. Let me know if you have any further questions!