Question

Micky is trying to solve the following problem but, he missed the lesson. In complete sentences, describe how you woukd solve the following problem. 6|2x-14|=42

Answer 1

We must solve for x.  Let's simplify this equation by dividing both sides by 6:

|2x-14|=7, which is the same as 2|x-7|=7.

First, assume that x-7 is already positive, so that we don't need the absolute value operator.  Then x-7=7/2.  Adding 7 to both sides results in x = 21/2.

Next, find the other solution:

Assume that x-7 is negative.  Then |x-7|=-(x-7).  Then -(x-7) = 7,

and -x + 7 = 7.  Thus, x = 0.

The solution set is {0, 21/2}.

Answer 2

First the two lines on either side of I2x-14I shows us that 2x-14 needs to be in the absolute form which would be 2x+14 because the absolute form is just referring to the numeral amount that a number or equation etc is from 0. Once you have done this you will now have 6(2x+14)=42. Now use the distributive property first multiplying 6 by 2x to come up with 12x then multiplying 6 with 14 to come up with 84. This leaves you with 12x+84=42. Next, subtract 84 from both sides of the equation to come up with 12x=-42. Finally, divide both sides of the equation by 12 to come up with x = -3.5