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,
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
