Solve inequality |2 x+10|26
It would help if you proofread your questions before you posted them.
There is no inequality given. An inequality requires either a < or > symbol.
To solve the inequality |2x + 10| < 26, we have two cases to consider: when the expression inside the absolute value is positive and when it is negative. Let's solve each case separately:
Case 1: (2x + 10) ≥ 0
If (2x + 10) ≥ 0, then the absolute value is unnecessary and we can rewrite the inequality as follows:
2x + 10 < 26
Now, let's solve for x:
2x < 26 - 10
2x < 16
x < 8
So, for the first case, the solution is x < 8.
Case 2: (2x + 10) < 0
If (2x + 10) < 0, we need to negate the expression inside the absolute value signs and rewrite the inequality:
-(2x + 10) < 26
Now, let's solve:
-2x - 10 < 26
-2x < 26 + 10
-2x < 36
x > -18 (Note: we flipped the inequality when multiplying by -1)
So, for the second case, the solution is x > -18.
Combining the solutions from both cases, we find that the inequality holds true when x is smaller than 8 or greater than -18. In interval notation, this can be expressed as:
(-∞, -18) ∪ (8, ∞)