Answer:
Inequality Notation: x < 1
See attached for the number line.
Step-by-step explanation:
To solve the inequality -5x + 8 > 3, use algebraic operations to isolate x.
Begin by subtracting 8 from both sides of the inequality:
[tex]\begin{aligned}-5x + 8-8& > 3-8\\\\-5x& > -5\end{aligned}[/tex]
Now, divide both sides of the inequality by -5, remembering that when we divide or multiply by a negative number, we need to reverse the inequality sign:
[tex]\begin{aligned}\dfrac{-5x}{-5}& > \dfrac{-5}{-5}\\\\x& < 1\end{aligned}[/tex]
Therefore, the solution to the given inequality is x < 1, which means that the solution set includes all values of x that are less than 1.
To graph the solution on a number line:
- Draw an open circle at 1, indicating that x = 1 is not part of the solution.
- Shade to the left to represent all x values less than 1.
- Add an arrowhead at the end of the shading pointing in the negative direction to indicate that the solution extends infinitely in that direction.
