Final answer:
To solve the linear inequality 23x - 4 < -13x - 5, add 13x to both sides and add 4 to both sides, simplify and then divide by 36 to find x < -1/36, which is the solution.
Step-by-step explanation:
To solve the linear inequality 23x - 4 < -13x - 5, we will first combine like terms. We do this by adding 13x to both sides of the inequality to bring all the x terms to one side and adding 4 to both sides to move the constant terms to the other side, resulting in:
23x - 4 + 13x + 4 < -13x - 5 + 13x + 4
This simplifies to 36x < -1. Then we will divide both sides of the inequality by 36 to solve for x:
x < -1/36
The solution to the inequality is all real numbers less than -1/36.