Q: solve using the addition and multiplication principles
2 + 8x < 10
{x|x ? ?}
A: {x|x < 1}
To solve the inequality 2 + 8x < 10, we can apply the addition and multiplication principles.
Step 1: Start by subtracting 2 from both sides of the inequality:
2 + 8x - 2 < 10 - 2
8x < 8
Step 2: Divide both sides of the inequality by 8 (the coefficient of x) to isolate x:
(8x)/8 < 8/8
x < 1
So the solution to the inequality 2 + 8x < 10 is x < 1.
Now let's express the solution set in set-builder notation:
{x| x < 1}
This represents the set of all values of x which are less than 1.