Solve.
$| x - 2 | + 8 = 11$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution(s) is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed)
B. There is no solution.

Answer

Expert–verified

Hide Steps

Answer

The final solutions to the equation are $5$ and $- 1$ .

Steps

Step 1 ：Rewrite the absolute value equation as two separate equations, one for when the value inside the absolute value is positive and one for when it is negative.

Step 2 ：For the positive case, the equation becomes $x - 2 + 8 = 11$ , which simplifies to $x + 6 = 11$ .

Step 3 ：Solving for $x$ in the positive case gives the solution $x = 5$ .

Step 4 ：For the negative case, the equation becomes $- (x - 2) + 8 = 11$ , which simplifies to $10 - x = 11$ .

Step 5 ：Solving for $x$ in the negative case gives the solution $x = - 1$ .

Step 6 ：The final solutions to the equation are $5$ and $- 1$ .

Solve.|x−2|+8=11 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution(s) is/are(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed)B. There is no solution.

Answer

Popular Problems

Solve.
$| x - 2 | + 8 = 11$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution(s) is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed)
B. There is no solution.