Question

1) 6 – 5х ≤ 2 2) 9 – 12х ≥ 0 3) 6 + х < 3 – 2х 4) 4х + 19 ≤ 5х – 1 4) 4х + 7 ≤ 6х + 1 5) 4 + 12х > 7 + 13х 6) 6х ≥ 8х + 1 7) 3(2 + х) > 4 – х 7) 4(1 + х) > х – 2 8) –(4 - х) ≤ 2(3 + х) 9 ) 3(1 - х) + 2(2 – 2х) < 0 10) –(2 – 3х) + 4(6 + х) ≥ 1

Answer 1

Ответ:

1)

6-5х≤2

-5х≤2-6

-5х≤-4

х≤-4:-5

х≤0,8

2)

9-12х≥0

-12x≥0-9

x≥-9:-12

x≥0,75

3)

6+x<3-2x

x+2x<3-6

3x<-3

x<-3:3

x<-1

4)

4х + 19 ≤ 5х – 1

4x-5x  ≤-1-19

-x ≤-20

x ≤20

5)

4 + 12x > 7 + 13х

12x-13x >7-4

-x >3

x >-3

6)

6х ≥ 8х + 1

6x-8x ≥1

-2x ≥1

x ≥1:-2

x ≥-0,5

7)

4(1 + х) > х – 2

4+4x >x-2

4x-x >-2-4

3x >-6

x >-6:3

x >-2

8)

–(4 - х) ≤ 2(3 + х)

-4+x≤6+2x

x-2x≤6+4

-x≤10

x≤-10

9)

3(1 - х) + 2(2 – 2х) < 0

3-3x+4-4x <0

3-3x-4x <0-4

-7x <-4-3

-7x <-7

x<1

10)

–(2 – 3х) + 4(6 + х) ≥ 1

-2+3x+24+4x≥1

-2+3x+4x≥-24

7x≥-23+2

7x≥-21

x≥-3

Answer 2

To solve these linear inequalities, we'll isolate the variable x in each inequality. Here are the solutions for each inequality:

1. $6 - 5x \leq 2$: Subtract 6 from both sides: $-5x \leq -4$ Divide by -5 (remember to reverse the inequality when dividing by a negative number): $x \geq \frac{4}{5}$

2. $9 - 12x \geq 0$: Subtract 9 from both sides: $-12x \geq -9$ Divide by -12 (reverse the inequality): $x \leq \frac{3}{4}$

3. $6 + x < 3 - 2x$: Add 2x to both sides: $6 + 3x < 3$ Subtract 6 from both sides: $3x < -3$ Divide by 3: $x < -1$

4. $4x + 19 \leq 5x - 1$: Subtract 4x from both sides: $19 \leq x - 1$ Add 1 to both sides: $20 \leq x$

5. $4 + 12x > 7 + 13x$: Subtract 13x from both sides: $4 - x > 7$ Subtract 4 from both sides: $-x > 3$ Multiply by -1 (reverse the inequality): $x < -3$

6. $6x \geq 8x + 1$: Subtract 8x from both sides: $6x - 8x \geq 1$ Simplify: $-2x \geq 1$ Divide by -2 (reverse the inequality): $x \leq -\frac{1}{2}$

7. $3(2 + x) > 4 - x$: Distribute the 3 on the left side: $6 + 3x > 4 - x$ Add x to both sides: $6 + 4x > 4$ Subtract 6 from both sides: $4x > -2$ Divide by 4: $x > -\frac{1}{2}$

8. $-(4 - x) \leq 2(3 + x)$: Distribute the 2 on the right side: $-(4 - x) \leq 6 + 2x$ Remove the parentheses on the left side (reverse the inequality when multiplying by -1): $x - 4 \leq 6 + 2x$ Subtract 2x from both sides: $-4 \leq 6 + x$ Subtract 6 from both sides: $-10 \leq x$

9. $3(1 - x) + 2(2 - 2x) < 0$: Distribute on both sides: $3 - 3x + 4 - 4x < 0$ Combine like terms: $-7x + 7 < 0$ Subtract 7 from both sides: $-7x < -7$ Divide by -7 (reverse the inequality): $x > 1$

10. $-(2 - 3x) + 4(6 + x) \geq 1$: Distribute on both sides: $-2 + 3x + 24 + 4x \geq 1$ Combine like terms: $7x + 22 \geq 1$ Subtract 22 from both sides: $7x \geq -21$ Divide by 7: $x \geq -3$

So, the solutions to the inequalities are:

1. $x \geq \frac{4}{5}$
2. $x \leq \frac{3}{4}$
3. $x < -1$
4. $x \geq 20$
5. $x < -3$
6. $x \leq -\frac{1}{2}$
7. $x > -\frac{1}{2}$
8. $x \geq -10$
9. $x > 1$
10. $x \geq -3$