Complete the two-column proof.
Given: x/5 + 9 = 11
Prove: x = 10
x/5 + 9 = 11 a.__________
x/5 = 2 b.__________
x = 10 c.__________
A) a. Given
b. Subtraction Property of Equality
c. Division Property of Equality
B) a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
C) a. Given
b. Addition Property of Equality
c. Multiplication Property of Equality
D) a. Given
b. Addition Property of Equality
c. Division Property of Equality
How would I go about doing this step-by-step? I'm a little stumped.
To complete the two-column proof, follow these steps:
Step 1: Given: Write down the given equation as a statement. In this case, the given equation is x/5 + 9 = 11.
Step 2: Choose the appropriate property: Determine which property of equality is being used in each step.
Step 3: Fill in the missing statements: Based on the given equation and the chosen property, fill in the missing statements in the proof.
Now let's go through the steps in this specific proof:
Given: x/5 + 9 = 11
To prove: x = 10
Step 1: Given
a. Given: x/5 + 9 = 11
Step 2: Choose the appropriate property
The first step in the proof is to isolate the variable x by eliminating the 9 on the left side of the equation.
To do this, we will use the Subtraction Property of Equality, which states that if a = b, then a - c = b - c.
Step 3: Fill in the missing statements
a. Given: x/5 + 9 = 11
b. Subtraction Property of Equality: (x/5 + 9) - 9 = 11 - 9
Simplify the left side by subtracting 9 from both sides:
(x/5) = 2
Now we want to further isolate the variable x, so we'll use the Division Property of Equality, which states that if a = b, then a/c = b/c (as long as c ≠ 0).
c. Division Property of Equality: (x/5) * 5 = 2 * 5
Simplify the left side by multiplying by 5:
x = 10
Thus, the complete two-column proof is:
a. Given: x/5 + 9 = 11
b. Subtraction Property of Equality: (x/5 + 9) - 9 = 11 - 9
c. Division Property of Equality: (x/5) * 5 = 2 * 5