Question

3(x+2)-4(x-6)>2(x-5)

Answer 1

3x+6-4x+24>2x-10

-1x+30>2x-10

Answer 2

Let's solve the inequality step by step:

3(x + 2) - 4(x - 6) > 2(x - 5)

First, let's simplify the equation by applying the distributive property:

3x + 6 - 4x + 24 > 2x - 10

Combine like terms on each side:

-x + 30 > 2x - 10

Next, let's isolate the variable terms on one side and the constant terms on the other side. We can do this by subtracting 2x from both sides:

-x - 2x + 30 > -10

Simplify further:

-3x + 30 > -10

Now, let's isolate the variable by subtracting 30 from both sides:

-3x > -10 - 30

Simplify further:

-3x > -40

To solve for x, we need to divide both sides of the inequality by -3. Remember that when we divide by a negative number, the inequality sign flips:

x < -40 / -3

Simplify the division:

x < 40/3

Therefore, the solution to the inequality 3(x + 2) - 4(x - 6) > 2(x - 5) is x < 40/3.