To solve the inequality 4x < 3 – 2x, we first need to isolate the variable on one side. We can start by adding 2x to both sides:
4x + 2x < 3
This simplifies to:
6x < 3
Next, we will divide both sides by 6:
x < rac{3}{6}
Which reduces to:
x < rac{1}{2}
This means that the solution set includes all numbers less than 0.5. On a number line, this would be represented by an open circle at 0.5 with a shaded line extending to the left, indicating that all values less than 0.5 are included in the solution.