Question

8(2x − 14) + 13 = 4x − 27

Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)

Part B: What value of x makes the equation true? (4 points)

Answer 1

Part A:

8(2x - 14) + 13 = 4x - 27

16x - 112 + 13 = 4x - 27     // expand

16x - 99 = 4x - 27           // combine like terms

12x - 99 = -27         // subtract 4x from both sides

12x = 72          // add 99 to both sides

x = 6           // divide by 12 on both sides

Part B:

x = 6

Answer 2

Answer:

Part A: The steps I will use to solve the equation will be:

Step 1: Simplify each side of the equation

So in this equation, we can see that on the left side of the equations, there are brackets, so our job is to solve the brackets:

8(2x - 14) + 13= 16x - 112 + 13

And then we can also see the number 13, so this side is not completely simplified yet, therefore we need to add -122 to 13 and the result will be -99.

Step 2: Move the variables to one side

So after our first step, we have:

16x - 99 = 4x - 27

In this step, we need to move all the x variables to one side (I would prefer the left side) and the numbers to the other side:

16x - 4x = 99 - 27

Step 3: Isolate the variables:

Now since we already saw that 16x and -4x have x as a common factor, we can just subtract 16 to 4, this gives us the results of 12x. Do the same thing with the right side, we subtract 99 to 27 to get 72.

Now we have: 12x = 72 ⇔ x = 72/12 = 6

Part B:

*If we just follow the steps above, we will have x = 6 as a result, and it is the only solution to the equation.

(I'm truly sorry if there is any grammar mistake, hope this help you)