We want to isolate the variable on one side and numbers on another side. Treat like a normal equation. 

 Add  and subtract  on both sides.

 Divide  on both sides.

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation. 

 We need to set-up two equations since its absolute value.

 Add  on both sides.

 Divide  on both sides.

 Divide  on both sides which flips the sign.

 Add  on both sides. 

 Divide  on both sides.

Since we have the 's being either greater than or less than the values, we can combine them to get .

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation. 

 We need to set-up two equations since it's absolute value.

 Add  on both sides.

 Divide  on both sides.

 Distribute the negative sign to each term in the parenthesis.

 Add  and subtract  on both sides.

 Divide  on both sides.

  We must check each answer. Let's try .

     This is not true therefore  is not correct. Let's try .

   This true so therefore  is correct. 

Final answer is .

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation. 

 We need to set-up two equations since it's absolute value.

 Subtract  and add  on both sides.

 Distribute the negative sign to each term in the parenthesis.

 Add  , on both sides.

 Divide  on both sides.

 We must check each answer. Let's try .

     This is not true therefore  is not correct. Let's try .

   This true so therefore  is correct. 

Final answer is .

Solve the inequality by adding 3 to both sides to get x < 12.  Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.

3w/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.

Absolute value problems always have two sides: one positive and one negative.

First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.

Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).

We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

First, solve the inequality :

Since we are dealing with absolute value,  must also be true; therefore:

To solve , isolate .

Divide by three on both sides.

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation. 

 Subtract  on both sides.

 Divide  on both sides. Remember to flip the sign.