What is the solution set to the inequality 5(-2x + 1) ≥ -2(4x - 5)?
Select a ray. Move the point on the ray to the correct place on the number line.
To solve the inequality, we can start by distributing the numbers on both sides:
5(-2x + 1) ≥ -2(4x - 5)
-10x + 5 ≥ -8x + 10
Next, we can combine like terms:
-10x + 8x ≥ 10 - 5
-2x ≥ 5
Now, we can divide both sides by -2, but since we are dividing by a negative number, we need to reverse the inequality sign:
x ≤ -5/2
So the solution set to the inequality is all x-values less than or equal to -5/2.
To represent this on a number line, we can select a ray that starts at -5/2 and goes to the left, including -5/2 and all numbers less than -5/2. We can then move the point to the correct place on the number line.