Question

1) 2x+3<x+1 2) 2-x<3x-10 3) 5x+2>3x+10​

Answer 1

Ответ:

1) $x$∈(-∞;-2); 2) $x$∈(3;∞); 3) $x$∈(4;∞).

Пошаговое объяснение:

$1)2x+3$

$x$∈(-∞;-2)

$2)2-x$

$x$∈(3;∞)

$3)5x+2>3x+10\\5x-3x>10-2\\2x>8\\x>4$

$x$∈(4;∞)

Answer 2

Certainly, I can help you solve these inequalities. Let's solve each one step by step:

1. $2x + 3 < x + 1$:

Subtract $x$ from both sides: $2x - x + 3 < x - x + 1$ $x + 3 < 1$

Subtract 3 from both sides: $x + 3 - 3 < 1 - 3$ $x < -2$

So, the solution for the first inequality is $x < -2$.

2. $2 - x < 3x - 10$:

Add $x$ to both sides: $2 - x + x < 3x + x - 10$ $2 < 4x - 10$

Add 10 to both sides: $2 + 10 < 4x - 10 + 10$ $12 < 4x$

Divide both sides by 4: $\frac{12}{4} < \frac{4x}{4}$ $3 < x$

So, the solution for the second inequality is $x > 3$.

3. $5x + 2 > 3x + 10$:

Subtract $3x$ from both sides: $5x - 3x + 2 > 3x - 3x + 10$ $2x + 2 > 10$

Subtract 2 from both sides: $2x + 2 - 2 > 10 - 2$ $2x > 8$

Divide both sides by 2: $\frac{2x}{2} > \frac{8}{2}$ $x > 4$

So, the solution for the third inequality is $x > 4$.

To summarize:

1. $x < -2$
2. $x > 3$
3. $x > 4$