Question

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:

Answer 1

The given equation is:

$\frac{2}{3}(x-9)+4\leq24-\frac{2}{3}x$

Step 2:

$\frac{2}{3}x-6+4\leq24-\frac{2}{3}x$

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:

$\frac{2}{3}x+\frac{2}{3}x\leq24+6-4$$\frac{4}{3}x\leq26$

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

$4x\leq26\times3$$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.