Question

3(1-x) - (2 - x) ≤ 2 10х-3(4-2х)>16+20х 2х-3(х+4)<х-12 6-6(х-3) ≥2(х+1)-10 3(х-2)-5(х+3)>27

Answer 1

Ответ:

Пошаговое объяснение:

1. 3(1-x) - (2 - x) ≤ 2

  3-3x-2+x ≤ 2

 -3x+x ≤ 2-3+2

   -2x≤ 1 |:(-2)

    х≥-0,5

2.10х-3(4-2х)>16+20х

  10х-12+6х>16+20х

  10х+6х-20х>16+12

 -4х>28 |:(-4)

   х<-7

3.2х-3(х+4)<х-12

  2х-3х-12<х-12

  2х-3х-х<-12+12

   -2х<0 |:(-2)

    х>0

4.6-6(х-3) ≥2(х+1)-10

  6-6х+18≥2х+2-10

  -6х-2х ≥2-10+6-18

   -8х≥-20 |:(-8)

    х≤ 2,5

5.3(х-2)-5(х+3)>27

  3х-6-5х-15>27

  3х-5х>27+6+15

  2х>48 |: 2

   х>24

Answer 2

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

1. $3(1-x) - (2 - x) \leq 2$

First, simplify the expressions on both sides:

$3 - 3x - 2 + x \leq 2$

Now, combine like terms:

$-2x + 1 \leq 2$

Next, subtract 1 from both sides to isolate the variable:

$-2x \leq 1$

Finally, divide by -2. Remember that when dividing by a negative number, you must reverse the inequality sign:

$x \geq -\frac{1}{2}$

So, the solution is $x \geq -\frac{1}{2}$.

2. $10x - 3(4-2x) > 16 + 20x$

First, distribute the -3 on the left side of the inequality:

$10x - 12 + 6x > 16 + 20x$

Combine like terms:

$16x - 12 > 16 + 20x$

Now, subtract 20x from both sides:

$-4x - 12 > 16$

Add 12 to both sides:

$-4x > 28$

Finally, divide by -4. Remember to reverse the inequality sign:

$x < -7$

So, the solution is $x < -7$.

3. $2x - 3(x + 4) < x - 12$

First, distribute the -3 on the left side of the inequality:

$2x - 3x - 12 < x - 12$

Combine like terms:

$-x - 12 < x - 12$

Now, add x to both sides:

$-12 < 2x - 12$

Add 12 to both sides:

$0 < 2x$

Finally, divide by 2:

$0 < x$

So, the solution is $x > 0$.

4. $6 - 6(x - 3) \geq 2(x + 1) - 10$

First, distribute the -6 on the left side of the inequality and the 2 on the right side:

$6 - 6x + 18 \geq 2x + 2 - 10$

Combine like terms:

$24 - 6x \geq 2x - 8$

Now, add 6x to both sides:

$24 \geq 8x - 8$

Add 8 to both sides:

$32 \geq 8x$

Finally, divide by 8:

$4 \geq x$

So, the solution is $x \leq 4$.

5. $3(x - 2) - 5(x + 3) > 27$

First, distribute the 3 on the left side and the -5 on the right side:

$3x - 6 - 5x - 15 > 27$

Combine like terms:

$-2x - 21 > 27$

Now, add 21 to both sides:

$-2x > 48$

Finally, divide by -2. Remember to reverse the inequality sign:

$x < -24$

So, the solution is $x < -24$.