1. Justify the solution to (x-5)=56+6(x-5) by matching a property to each step.
Step 1: -4(X-5)=56
Step 2: X-5=14
Step 3: X=-9
A addition property of equality
B subtraction property of equality
C multiplication property of equality
D division property of equality
E distributive property
the steps appear to be ... B, D, A
but the numbers don't match (starting with Step 1)
perhaps multiple typos?
To justify the solution to the equation (x-5)=56+6(x-5) by matching a property to each step, we will analyze each step:
Step 1: -4(X-5)=56
Here, we apply the distributive property. The distributive property states that a(b + c) = ab + ac. In this step, we distribute the -4 to both terms inside the parentheses, yielding -4x + 20 = 56.
Step 2: X-5=14
The next step involves applying the subtraction property of equality. The subtraction property of equality states that if a = b, then a - c = b - c. In this step, we subtract 20 from both sides of the equation, resulting in -4x = 36.
Step 3: X=-9
Lastly, we use the division property of equality. The division property of equality states that if a = b, and c is not zero, then a/c = b/c. In this step, we divide both sides of the equation by -4 to isolate the variable x, which gives us x = -9.
So, by matching the steps to their corresponding properties:
Step 1: E - distributive property
Step 2: B - subtraction property of equality
Step 3: D - division property of equality
Therefore, the solution to the equation is x = -9.