Question

1) 2x>-7,22) 1/2x+3≤2x-13) 3(2x-4)≤-5(2-3x)

Answer 1

1) 2x>-7,2
x > -3,6
2) 1/2x+3≤2x-1
Умножаем обе части на 2
x+6≤4x-2
x-4x≤-2-6
-3x ≤ -8

$x \geqslant \frac{3}{8}$
3) 3(2x-4)≤-5(2-3x)
6x-12≤-10+15x
6x-15x≤-10+12
-9x≤2
9x≥-2

$x \geqslant - \frac{2}{9}$

Answer 2

Let's solve each of these inequalities step by step:

1. $2x > -7$ To solve this inequality, you can divide both sides by 2. However, since you are dividing by a positive number, the inequality sign remains the same.

$x > -7/2$

So, the solution to this inequality is $x > -\frac{7}{2}$.

2. $\frac{1}{2}x + 3 \leq 2x - 1$ To solve this inequality, you can start by subtracting $\frac{1}{2}x$ from both sides of the inequality:

$3 \leq \frac{3}{2}x - 1$

Next, add 1 to both sides:

$4 \leq \frac{3}{2}x$

Now, divide both sides by $\frac{3}{2}$, which is the same as multiplying by $\frac{2}{3}$:

$\frac{4}{\frac{3}{2}} \leq x$

To simplify the left side, multiply the numerator and denominator of $\frac{4}{\frac{3}{2}}$ by 2:

$\frac{8}{3} \leq x$

So, the solution to this inequality is $x \geq \frac{8}{3}$.

3. $3(2x - 4) \leq -5(2 - 3x)$ First, distribute on both sides:

$6x - 12 \leq -10 + 15x$

Next, move the terms with x to one side and the constants to the other side. You can do this by subtracting 6x and adding 10 to both sides:

$-12 + 10 \leq 15x - 6x$

$-2 \leq 9x$

Now, divide both sides by 9. Since you are dividing by a positive number, the inequality sign remains the same:

$-\frac{2}{9} \leq x$

So, the solution to this inequality is $x \geq -\frac{2}{9}$.

To summarize:

1. $x > -\frac{7}{2}$
2. $x \geq \frac{8}{3}$
3. $x \geq -\frac{2}{9}$