Question

Solve the inequality: 3(x−2)<2x+1.

Answer 1

To solve the inequality 3(x−2)<2x+1, distribute the 3, collect like terms, and isolate x to find that x must be less than 7.

Step-by-step explanation:

To solve the inequality 3(x−2)<2x+1, start by distributing the 3 to both terms inside the parentheses:

3x - 6 < 2x + 1

Next, get all x terms on one side and constant terms on the other:

3x - 2x < 1 + 6

This simplifies to:

x < 7

The solution to the inequality is all x values that are less than 7. To visualize this, you can draw a number line and shade all the points to the left of 7 but not including 7 itself.

Answer 2

To solve the inequality 3(x-2) < 2x + 1, we will simplify and isolate the variable x.

Let's start by distributing 3 to the terms inside the parentheses:

3x - 6 < 2x + 1

Next, we want to isolate the x term on one side of the inequality. We can do this by subtracting 2x from both sides:

3x - 2x - 6 < 2x - 2x + 1

Simplifying further:

x - 6 < 1

Now, we add 6 to both sides of the inequality to isolate the x term:

x - 6 + 6 < 1 + 6

Simplifying:

x < 7

Therefore, the solution to the inequality 3(x-2) < 2x + 1 is x < 7.