Solve and graph the inequality. |x + 6| >= 7 Choose the correct answer below.
A. x >= 1 B. - 13 <= x <= 1 O C. x <= - 13 or x >= 1 D. x <= - 7 or x >= 7
To solve the inequality |x + 6| >= 7, we need to separate it into two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: x + 6 >= 7
Solving for x, we subtract 6 from both sides:
x >= 1
Case 2: -(x + 6) >= 7
Solving for x, we first distribute the negative sign:
-x - 6 >= 7
Next, we add 6 to both sides:
-x >= 13
To solve for -x, we multiply both sides by -1 and reverse the inequality symbol:
x <= -13
Combining the solutions from both cases, the answer is B. -13 <= x <= 1.
To graph the inequality, we can plot the range of x values, which is from -13 to 1, and shade the area between these values on a number line.
To solve the inequality |x + 6| >= 7, we need to consider two cases: x + 6 >= 7 and x + 6 <= -7.
1. Case 1: x + 6 >= 7
Solving this case gives us x >= 1.
2. Case 2: x + 6 <= -7
Solving this case gives us x <= -13.
Therefore, the solution to the inequality |x + 6| >= 7 is x <= -13 or x >= 1. So the correct answer is C.
To solve the inequality |x + 6| >= 7, we can break it down into two separate inequalities:
1. x + 6 >= 7
2. x + 6 <= -7
Let's solve each of these inequalities:
1. x + 6 >= 7:
Subtract 6 from both sides: x + 6 - 6 >= 7 - 6
Simplify: x >= 1
2. x + 6 <= -7:
Subtract 6 from both sides: x + 6 - 6 <= -7 - 6
Simplify: x <= -13
Now we can combine the solutions to both inequalities to find the final solution. Since it is an "or" inequality (|x + 6| >= 7), the solution will involve both parts of the solution separately:
The correct answer is option C: x <= -13 or x >= 1.
Now let's graph the solution on a number line:
------o----------------o-----------------
-13 1
The shaded regions indicate the values of x that satisfy the inequality.