Solve the inequality |2x+10|>26
Ah, better!
l2xl > 16
x > ± 8
To solve the inequality |2x+10|>26, we need to consider two cases: one where the expression inside the absolute value is positive (2x+10 > 26), and another where it is negative (−(2x+10) > 26).
Case 1: 2x + 10 > 26
To solve this inequality, we can start by subtracting 10 from both sides:
2x > 26 - 10
2x > 16
Then, divide both sides by 2 to isolate the x variable:
x > 8
Case 2: -(2x + 10) > 26
In this case, we need to distribute the negative sign to both terms inside the parentheses:
-2x - 10 > 26
Next, add 10 to both sides to isolate the -2x term:
-2x > 26 + 10
-2x > 36
Now, divide both sides by -2. However, whenever we multiply or divide both sides of an inequality by a negative number, the inequality flips. So the direction of the inequality changes:
x < 36 / -2
x < -18
Therefore, the solution to the inequality |2x+10|>26 is x > 8 or x < -18.