How do you solve #|10x + 2| - 18 = -12#?

First, before I solve the equation, let me prove the point I made above to further your understanding.

Let's look at an extremely simple equation involving absolute value.

An absolute value, by definition, means the distance on the number line between 0 and the number. This distance doesn't take into account direction and therefore always is positive.

So, we must consider in the above equation the following:

x = 2 or -x = 2

x = 2 or x = -2

Solving your equation:

We must first isolate the absolute value:

Hopefully this helps, and happy voting tomorrow!

To solve the equation ( |10x + 2| - 18 = -12 ), you would first isolate the absolute value expression by adding 18 to both sides of the equation. Then, you would solve for ( |10x + 2| ) by setting it equal to the resulting constant on the other side. Finally, you would solve for ( x ) by considering both the positive and negative cases of the absolute value expression. So, the steps are:

1. ( |10x + 2| - 18 + 18 = -12 + 18 )
2. ( |10x + 2| = 6 )
3. Solve for positive case: ( 10x + 2 = 6 )
4. Solve for negative case: ( -(10x + 2) = 6 )

To solve the equation |10x + 2| - 18 = -12, you would follow these steps:

1. Add 18 to both sides of the equation: |10x + 2| = 6.
2. Break the equation into two separate equations: 10x + 2 = 6 and 10x + 2 = -6.
3. Solve each equation separately.
4. For the first equation (10x + 2 = 6), subtract 2 from both sides and then divide by 10: x = 0.4.
5. For the second equation (10x + 2 = -6), subtract 2 from both sides and then divide by 10: x = -0.8.

So, the solutions to the equation |10x + 2| - 18 = -12 are x = 0.4 and x = -0.8.