Question

Question 2(Multiple Choice Worth 4 points) (01.02 LC) The equation 8x − 12 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. What is the distance, in miles, between the cars? x = 48 x = 30 x = 3 x = 1

Answer 1

To find the distance between the two cars, we need to solve the equation 8x - 12 = 4x.

Subtract 4x from both sides to isolate the x term:

8x - 4x - 12 = 4x - 4x

4x - 12 = 0

Now, add 12 to both sides to get the x term alone on one side of the equation:

4x - 12 + 12 = 0 + 12

4x = 12

Finally, divide both sides by 4 to solve for x:

4x / 4 = 12 / 4

x = 3

So, the distance between the two cars is x = 3 miles. Therefore, the correct answer is:

x = 3 miles.

Answer 2

x = 3 miles

Explanation:

We can solve the equation 8x − 12 = 4x and find the distance between the cars by:

`\sf 8x - 12 = 4x`

Subtracting 4x from both sides of the equation.

`\sf 8x - 12 -4x = 4x -4x`

`\sf 4x -12 =0`

Adding 12 to both sides of the equation.

`\sf 4x - 12 +12= 12`

`\sf \sf 4x = 12`

Divide both sides of the equation by 4.

`\sf (4x)/(4)=(12)/(4)`

`\sf x = 3`

Since x represents the distance in miles between the cars, the distance between the cars is 3 miles.

Therefore, the distance between the cars is 3 miles.