Austin and Lisa worked out the same problem
5x - 3(x-2) = 8
Austin’s answer was X=7
Lisa’s answer was X = 1
Who is correct, or are they both wrong? Why
To determine who is correct, we need to substitute their answers back into the original equation and see if it holds true.
Substituting Austin's answer, x = 7, into the equation:
5(7) - 3(7-2) = 8
35 - 3(5) = 8
35 - 15 = 8
20 = 8
This equation is not true, so Austin's answer is incorrect.
Substituting Lisa's answer, x = 1, into the equation:
5(1) - 3(1-2) = 8
5 - 3(-1) = 8
5 + 3 = 8
8 = 8
This equation is true, so Lisa's answer is correct.
Therefore, Lisa is correct and Austin is incorrect.
To determine who is correct, we can solve the equation step by step:
Given equation: 5x - 3(x-2) = 8
First, let's simplify the equation by distributing the -3:
5x - 3x + 6 = 8
2x + 6 = 8
Next, we can isolate the variable x by subtracting 6 from both sides:
2x + 6 - 6 = 8 - 6
2x = 2
To find the value of x, we divide both sides of the equation by 2:
2x/2 = 2/2
x = 1
Therefore, Lisa's answer of x = 1 is correct, and Austin's answer of x = 7 is incorrect.
In conclusion, Austin is wrong, while Lisa is correct.
To determine who is correct or if they are both wrong, we can solve the given equation using both Austin's and Lisa's solutions and see which solution satisfies the equation.
The equation is: 5x - 3(x-2) = 8
Step 1: Distribute the -3 to the terms inside the parentheses:
5x - 3x + 6 = 8
Step 2: Combine like terms:
2x + 6 = 8
Step 3: Move the constant term to the other side of the equation by subtracting 6 from both sides:
2x = 8 - 6
2x = 2
Step 4: Divide both sides of the equation by 2 to solve for x:
x = 2/2
x = 1
So, the correct solution to the equation is x = 1, which matches Lisa's answer. Austin's answer of x = 7 does not satisfy the equation.
Therefore, Lisa is correct, and Austin is wrong in this case.