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.
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
1 answer
1 answer