Question

976. 1) 17+ 2x > 5+X, 3x + 2 < 8 + x;(2) (1 – 0,5x < 4 – x,19-2, 8x > 6-1,3x;3) (0,4x - 1<0,5x - 1,7,2,7% -10 < 0,9x - 1;4) 12,8x -17 > 0,3x - 4,5,12,3x - 16,6 <7,1x +19,8.​

Answer 1

Пошаговое объяснение:

{17+2х>5+х

{3х+2<8+х

{2х-х>5-17

{3х-х<8-2

{Х> - 12

{2х<6

{Х> - 12

{Х<6:2

{Х>-12

{Х<3

Ответ : х€(-12;3)

2.

{1-0,5х<4-х

{19-2,8х>6-1,3х

{-0,5х+х<4-1

{-2,8х+1,3х>6-19

{0,5х<3

{-1,5х> - 13

{Х<3:0,5

{Х< - 13:(-1,5)

{Х<6

{Х<8 2/3

Ответ :(-бесконечности;6)

3.

{0,4х-1<0,5х-1,7

{2,7х-10<0,9х-1

{0,4х-0,5х< - 1,7+1

{2,7х-0,9х< - 1+10

{-0,1х< - 0,7

{1,8х<9

{Х> - 0,7:(-0,1)

{З<9:1,8

{Х>7

{Х<5

Ответ :нет решений

4.

{12,8х-17>0,3х-4,5

{12,3х-16,6<7,1х+19,8

{12,8х-0,3х> - 4,5+17

{12,3х-7,1х<19,8+16,6

{12,5х>12,5

{5,2х<36,4

{Х>12,5:12,5

{Х<36,4:5,2

{Х>1

{Х<7

Ответ : х€(1;7)

Answer 2

To solve each of the given inequalities, let's go through them one by one:

1. $17 + 2x > 5 + x$

First, we'll subtract $x$ from both sides:

$17 + x > 5$

Next, subtract $17$ from both sides:

$x > -12$

So, the solution is $x > -12$.

2. $1 - 0.5x < 4 - x$

First, we'll add $x$ to both sides:

$1 + 0.5x < 4$

Next, subtract $1$ from both sides:

$0.5x < 3$

Finally, multiply both sides by $2$ to isolate $x$:

$x < 6$

So, the solution is $x < 6$.

3. $19 - 2.8x > 6 - 1.3x$

First, we'll add $1.3x$ to both sides:

$19 - 1.3x > 6 + 1.5x$

Next, subtract $19$ from both sides:

$-1.3x > -13 + 1.5x$

Now, add $1.3x$ to both sides:

$0.2x > -13$

Finally, divide both sides by $0.2$ to isolate $x$:

$x > -65$

So, the solution is $x > -65$.

4. $0.4x - 1 < 0.5x - 1.7$

First, we'll add $1.7$ to both sides:

$0.4x + 0.7 < 0.5x$

Next, subtract $0.4x$ from both sides:

$0.7 < 0.1x$

Finally, divide both sides by $0.1$ to isolate $x$:

$7 < x$

So, the solution is $x > 7$.

5. $2.7\% - 10 < 0.9x - 1$

First, we'll add $10$ to both sides:

$2.7\% < 0.9x + 9$

Next, subtract $9$ from both sides:

$2.7\% - 9 < 0.9x$

Now, divide both sides by $0.9$ to isolate $x$:

$-6.3\% < x$

Since percentages are always between $-100\%$ and $100\%$, this inequality is true for all real numbers $x$.

6. $12.8x - 17 > 0.3x - 4.5$

First, add $4.5$ to both sides:

$12.8x - 12.5 > 0.3x$

Next, subtract $0.3x$ from both sides:

$12.5x - 12.5 > 0$

Finally, divide both sides by $12.5$ to isolate $x$:

$x > 1$

So, the solution is $x > 1$.

7. $12.3x - 16.6 < 7.1x + 19.8$

First, subtract $7.1x$ from both sides:

$5.2x - 16.6 < 19.8$

Next, add $16.6$ to both sides:

$5.2x < 36.4$

Finally, divide both sides by $5.2$ to isolate $x$:

$x < 7$

So, the solution is $x < 7$.

In summary:

1. $x > -12$
2. $x < 6$
3. $x > -65$
4. $x > 7$
5. True for all $x$
6. $x > 1$
7. $x < 7$