Solve the inequality. Graph the solution set and write it in interval notation.
6x-5>5x-8
To solve the inequality, we want to isolate the variable on one side of the inequality sign.
Starting with the given inequality: 6x - 5 > 5x - 8
First, we can combine like terms on both sides:
6x - 5x - 5 > -8
Simplifying, we have:
x - 5 > -8
Next, we can add 5 to both sides to further isolate the variable:
x - 5 + 5 > -8 + 5
Simplifying, we have:
x > -3
So the solution to the inequality is x > -3.
Graphing this solution on a number line, we would have an open circle at -3 and an arrow pointing to the right.
In interval notation, the solution set is (-3, ∞), meaning the interval of all real numbers greater than -3.