Question

(1)2+x>8-x (2) 2x+1>x+6 (3) 6 x+1 < 2x+9 (20 баллов)

Answer 1

Відповідь:

Покрокове пояснення:

1) x+x>8-2        2x>6      x>3     xє(3;∞)

2) 2x-x>6-1         x>5       xє(5;∞)

3) 6x-2x<9-1      4x<8      x<2       xє(-∞;2)

Answer 2

To solve these inequalities, we'll go through each one step by step:

(1) 2 + x > 8 - x:

Let's simplify the inequality:

2 + x > 8 - x

Combining like terms:

2x > 6 - x

Now, let's isolate x by moving the x term to one side:

2x + x > 6

3x > 6

Divide both sides by 3 to solve for x:

x > 2

Therefore, the solution to the inequality is x > 2.

(2) 2x + 1 > x + 6:

Let's simplify the inequality:

2x + 1 > x + 6

Subtract x from both sides:

x + 1 > 6

Subtract 1 from both sides:

x > 5

Therefore, the solution to the inequality is x > 5.

(3) 6x + 1 < 2x + 9:

Let's simplify the inequality:

6x + 1 < 2x + 9

Subtract 2x from both sides:

4x + 1 < 9

Subtract 1 from both sides:

4x < 8

Divide both sides by 4 to solve for x:

x < 2

Therefore, the solution to the inequality is x < 2.

Summary of solutions:

1. x > 2
2. x > 5
3. x < 2