Question

1) 5−3 х ≤ 80 2) 6 х+2>3 х−7

Answer 1

Ответ:

1)5-3x≤80

-3x≤80-5

-3x≤75

x≥-25

(-25;+∞)

2)6x+2>3x-7

6x-3x>-7-2

3x>-9

x>-3

(-3;+∞)

Answer 2

Let's solve these inequalities:

1. $5 - 3x \leq 80$

To solve this inequality, you want to isolate $x$ on one side of the inequality sign. Here's how you can do it:

Subtract 5 from both sides of the inequality:

$5 - 3x - 5 \leq 80 - 5$

This simplifies to:

$-3x \leq 75$

Now, divide both sides by -3. When you divide or multiply an inequality by a negative number, you need to reverse the inequality sign:

$-3x / -3 \geq 75 / -3$

This simplifies to:

$x \geq -25$

So, the solution for this inequality is $x \geq -25$.

2. $6x + 2 > 3x - 7$

To solve this inequality, you want to isolate $x$ on one side of the inequality sign. Here's how you can do it:

Subtract $3x$ from both sides of the inequality:

$6x - 3x + 2 > 3x - 3x - 7$

This simplifies to:

$3x + 2 > -7$

Now, subtract 2 from both sides:

$3x + 2 - 2 > -7 - 2$

This simplifies to:

$3x > -9$

Finally, divide both sides by 3:

$\frac{3x}{3} > \frac{-9}{3}$

This simplifies to:

$x > -3$

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