Question

DE=5x+6, AC=12x+8. What is the length of AC?

Answer 1

Your answer is AC = 32 units

Explanation:

The DE is half of AC and to find the length of AC, you have to multiply the length of DE by 2.

DE = 5x + 6

So,

2(5x + 6) = AC

Then after you divide, you have to distribute the 2 inside of the parentheses:

10x + 12

Now you always have to make the value equal to the expression because it's important:

AC = 12x + 8.

And 10x + 12 = 12x + 8

After that, you have to subtract the 10x from both sides of the equation to make it equal: 12 = 2x + 8

Subtract 8 from both sides of the equation to make this part of it equal too:

4 = 2x

Then you must divide both sides by 2 to solve for x: x = 2

So, the next step is to take the value of x and substitute it into the expression so you can find the length of AC: 12(2) + 8

Then the last step is to multiply 12 and 2 together: 24 + 8 and after that you add 24 and 8

24 + 8 = 32

So finally the answer is - AC = 32 units

Answer 2

AC = 32 units

Explanation:

It looks like DE is half of AC, so to find the length of AC you would multiply the length of DE by 2.

DE = 5x + 6, so 2(5x + 6) = AC.

Distribute the 2 inside the parentheses.

• 10x + 12

Now make this value equal to the expression standing for AC, 12x + 8.

• 10x + 12 = 12x + 8

Subtract 10x from both sides of the equation.

• 12 = 2x + 8

Subtract 8 from both sides of the equation.

• 4 = 2x

Divide both sides by 2 to solve for x.

• x = 2

Take this value of x and substitute it into the expression for the length of AC.

• 12(2) + 8

Multiply 12 and 2 together.

• 24 + 8

Add 24 and 8.

• 32

AC = 32 units