Question

Justify the first step that David took in verifying that x = 5 is a solution for the equation

8x – 13 = 2x + 17.

8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.

Answer 1

Step by step I don't see the correct first step.

Explanation:

Solve for x:

8 x - 13 = 2 x + 17

Hint: | Move terms with x to the left hand side.

Subtract 2 x from both sides:

(8 x - 2 x) - 13 = (2 x - 2 x) + 17

Hint: | Combine like terms in 8 x - 2 x.

8 x - 2 x = 6 x:

6 x - 13 = (2 x - 2 x) + 17

Hint: | Look for the difference of two identical terms.

2 x - 2 x = 0:

6 x - 13 = 17

Hint: | Isolate terms with x to the left hand side.

Add 13 to both sides:

6 x + (13 - 13) = 13 + 17

Hint: | Look for the difference of two identical terms.

13 - 13 = 0:

6 x = 17 + 13

Hint: | Evaluate 17 + 13.

17 + 13 = 30:

6 x = 30

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 6 x = 30 by 6:

(6 x)/6 = 30/6

Hint: | Any nonzero number divided by itself is one.

6/6 = 1:

x = 30/6

Hint: | Reduce 30/6 to lowest terms. Start by finding the GCD of 30 and 6.

The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:

Answer: x = 5