Question 4
The error was that in step 2, when distributing -3 into the parentheses, the person did not change the sign of 24 so that it was negative, since a negative number multiplied by a positive number will always make a negative number. Here is the correct way to solve this equation:
[tex]-5x+12-7x=-3(5x+8)\\-12x+12=-3(5x+8)[/tex]
Distrubute -3 into the parentheses
[tex]-12x+12=-15x-24[/tex]
Subtract both sides by 12
[tex]-12x+12-12=-15x-24-12\\-12=-15x-36[/tex]
Add 15x to both sides
[tex]-12+15x=-15x-36+15x\\3x=-36[/tex]
Divide both sides by 3
[tex]\frac{3x}{3} =\frac{-36}{3} \\x=-12[/tex]
Question 5
The error was that 2 was added on both sides in step 5 instead of being subtracted from both sides. Here is the correct way to do it, starting from step 4:
[tex]10=16x+2[/tex]
Subtract both sides by 2
[tex]10-2=16x+2-2\\8=16x[/tex]
Divide both sides by 16
[tex]\frac{8}{16} =\frac{16x}{16} \\\frac{1}{2}=x[/tex]
I hope this helps!
