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
13x/13 = 80/12
x = 6 2/13
Liam made a mistake in the step: 13x + 3 - 3 = 83 - 3
The correct step should be: 13x + 3 - 3 = 83 - 3 = 80
So, he should have written: 13x + 0 = 80 instead of 13x = 80
Should he have subtracted 13 from both sides of the equation rather than dividing, did he forget to distribute the 6 to the 3. or should he have added 3 to both sides of the equation rather than subtracting
Liam made a mistake by dividing both sides of the equation by 13 instead of subtracting 3 from both sides of the equation.
The correct step should have been: 13x + 3 - 3 = 83 - 3
By subtracting 3 from both sides, he would have gotten: 13x = 80.
Then, dividing both sides by 13, he would get the correct solution: x = 80/13.
sure?
Apologies for the confusion. Upon reviewing the steps again, it appears that Liam made multiple errors in his work.
The first error occurred when Liam distributed the 6 to both terms within the parentheses. The correct step should have been:
7x + 6(x + 3) = 83
7x + 6x + 18 = 83
Then, when combining like terms, the correct calculation should be:
13x + 18 = 83
To isolate the variable, he should have subtracted 18 from both sides:
13x + 18 - 18 = 83 - 18
13x = 65
Finally, by dividing both sides by 13, the correct solution would be:
x = 65/13
x = 5
Therefore, the mistake Liam made was forgetting to distribute the 6 to the terms inside the parentheses. He also made a mistake in his final calculation. The correct solution is x = 5.