Question

A)3(x+1)-2*(2-x)> -11б)(x+3)*(x-3) < (x+3)²

Answer 1

Вот решение. Удачи :)

Answer 2

Let's solve each inequality step by step:

A) 3(x + 1) - 2*(2 - x) > -11

Step 1: Distribute the terms inside the parentheses. 3x + 3 - 4 + 2x > -11

Step 2: Combine like terms. 5x - 1 > -11

Step 3: Add 1 to both sides to isolate the variable term. 5x > -10

Step 4: Divide both sides by 5 to solve for x. x > -2

So the solution for the inequality is x > -2.

B) (x + 3)*(x - 3) < (x + 3)²

Step 1: Expand the terms on both sides. x^2 - 9 < x^2 + 6x + 9

Step 2: Move all terms to one side to set the inequality to zero. x^2 - x^2 - 6x - 9 < 0

Step 3: Simplify the equation. -6x - 9 < 0

Step 4: Add 9 to both sides to isolate the variable term. -6x < 9

Step 5: Divide both sides by -6, remembering to reverse the inequality when dividing by a negative number. x > -9/6

Step 6: Simplify the fraction. x > -3/2

So the solution for the inequality is x > -3/2.

To summarize:

A) The solution for the inequality 3(x + 1) - 2*(2 - x) > -11 is x > -2.

B) The solution for the inequality (x + 3)*(x - 3) < (x + 3)² is x > -3/2.