153,258 views
31 votes
31 votes
The process below shows how Pete the Pi-rate approached solving an inequality:Step 12/3 (x-9)+4≤24- 2/3 xThis is the given equation.Step 22/3 x-6+4≤24-2/3 xI distributed 2/3Step 32/3 x-2≤24-2/3 xI combined like terms.Step 42x-6≤24-2xI multiplied everything by 3Step 5-6≤24-4xI subtracted 2x from both sidesStep 6-18≤-4xI subtracted 24 from both sidesStep 7 4.5≤xI divided both sides by -4Pete made 3 errors in his work. Identify which steps he committed the errors on and why they are incorrect:Error 1:Error 2: Error 3:

The process below shows how Pete the Pi-rate approached solving an inequality:Step-example-1
User Mattacular
by
2.8k points

1 Answer

16 votes
16 votes

The given equation is:


(2)/(3)(x-9)+4\leq24-(2)/(3)x

Step 2:


(2)/(3)x-6+4\leq24-(2)/(3)x

Step 2 is correct. In step 3 he says "I combined like terms". In this case, we have to consider the numbers that have 'x' and the ones that don't have. So, step 3 is wrong. The correct step 3 would be:


(2)/(3)x+(2)/(3)x\leq24+6-4
(4)/(3)x\leq26

Step 4 is correct, you can multiply both sides by 3:


4x\leq26*3
4x\leq78

Step 5 is wrong. There is no need to do that! Also step 6 is wrong too for the same reason. And finally, step 7 is correct, you can divide both sides by 4:


x\leq19.5

Answer: Steps 3, 4, and 5 are wrong. Step 3 is wrong because "we have to consider the numbers that have 'x' and the ones that don't have". Steps 4 and 5 are wrong because there is no need to do these steps. You can solve the inequation without them.

User Mujahid Bhoraniya
by
3.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.