Liam is solving the equation 7x+6(x+3)=83 . His steps are shown below. What mistake did Liam make while solving? 7x+6(x+3)=83 7x+6x+3=83 13x+3=83 13x+3−3=83−3 13x=80 13x13=8013 x=6213 (1 point) Responses Liam forgot to distribute the 6 to the 3. Liam forgot to distribute the 6 to the 3. Liam did everything correctly. Liam did everything correctly. Liam should have added 3 to both sides of the equation rather than subtracting. Liam should have added 3 to both sides of the equation rather than subtracting. Liam should have subtracted 13 from both sides of the equation rather than dividing. Liam should have subtracted 13 from both sides of the equation rather than dividing.
1 answer
The mistake Liam made is that he forgot to distribute the 6 to the 3 in the equation \(6(x+3)\).
Here’s the breakdown of his steps:
Start with the equation:
\(7x + 6(x + 3) = 83\)
Correctly distribute the 6:
\(7x + 6x + 18 = 83\) (not \(7x + 6x + 3\))
Combine like terms:
\(13x + 18 = 83\)
From that point, he would proceed to subtract 18 from both sides:
\(13x = 83 - 18\)
\(13x = 65\)
Finally, divide by 13:
\(x = 5\)
So the correct response is: Liam forgot to distribute the 6 to the 3.
