Question

Решите неравенство: 1) а) 17+x>37; б) 5-x≤1; в) 6,2+x≥10; г) 0,6-2х<0; 2) а) 1+6x<7; б) 6x+1>0; в) 3-2x≤8; г) 6-15x≥0; 3) а) 4+x<1-2x; б) 2+6x>5+7x; в) 4x+7≤6x+1; г) 9x≥4x+2; 4) а) 4(1+x)>x-2; б) -(2x+1)≤3(x+2); в) 6(2x-1)-(2+x)<0; г) 4(1-x)+5(x+8)≥0;

Answer 1

1.
а) 17 + x > 37
x > 37 - 17
x > 20

б) 5 - x ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x  ≥ 4

в) 6,2 + x ≥ 10
x ≥ 10 - 6,2
x ≥ 3,8

г) 0,6 - 2x < 0
-2x < -0,6
x > 0,3

2.
а) 1 + 6x < 7
6x < 6
x < 1

б) 6x + 1 > 0
6x > -1
x > -1/6

в) 3 - 2x ≤ 8
-2x ≤ 5
x ≥ -2,5

г) 6 - 15x ≥ 0
-15x ≥ -6
x ≤ 6/15
x ≤ 2/5

3.

а) 4 + x < 1 - 2x
x + 2x < 1 - 4
3x < -3
x < -1

б) 2 + 6x > 5 + 7x
6x - 7x > 3
-x > 3
x < -3

в) 4x + 7 ≤ 6x + 1
4x - 6x ≤ -6
x ≥ 3

г) 9x ≥ 4x + 2
5x ≥ 2
x ≥ 0,4

4.
a) 4(1+x) > x - 2
4 + 4x > x - 2
3x > -6
x > -2

б) -(2x - 1) ≤ 3(x + 2)
-2x + 1 ≤ 3x + 6
-5x ≤ 5
x ≥ -1

в) 6(2x - 1) - (2 + x) < 0
12x - 6 - 2 - x < 0
11x < 8
x < 8/11

г)   4(1 - x) + 5(x + 8) ≥ 0
4 - 4x + 5x + 40 ≥ 0
x ≥ -44

Answer 2

a) 17 + x > 37 Subtracting 17 from both sides: x > 37 - 17 x > 20

b) 5 - x ≤ 1 Adding x to both sides: 5 ≤ 1 + x Subtracting 1 from both sides: 4 ≤ x

c) 6.2 + x ≥ 10 Subtracting 6.2 from both sides: x ≥ 10 - 6.2 x ≥ 3.8

d) 0.6 - 2x < 0 Adding 2x to both sides: 0.6 < 2x Dividing both sides by 2: 0.3 < x

a) 1 + 6x < 7 Subtracting 1 from both sides: 6x < 7 - 1 6x < 6 Dividing both sides by 6: x < 1

b) 6x + 1 > 0 Subtracting 1 from both sides: 6x > -1 Dividing both sides by 6: x > -1/6

c) 3 - 2x ≤ 8 Subtracting 3 from both sides: -2x ≤ 8 - 3 -2x ≤ 5 Dividing both sides by -2 (note the change in the direction of the inequality): x ≥ -5/2

d) 6 - 15x ≥ 0 Adding 15x to both sides: 6 ≥ 15x Dividing both sides by 15 (note the change in the direction of the inequality): x ≤ 6/15 x ≤ 2/5

a) 4 + x < 1 - 2x Adding 2x to both sides: 4 + 3x < 1 Subtracting 4 from both sides: 3x < -3 Dividing both sides by 3: x < -1

b) 2 + 6x > 5 + 7x Subtracting 6x from both sides and subtracting 5 from both sides: -3 > x

c) 4x + 7 ≤ 6x + 1 Subtracting 4x from both sides and subtracting 7 from both sides: 0 ≤ 2x - 6 Adding 6 to both sides: 6 ≤ 2x Dividing both sides by 2: 3 ≤ x

d) 9x ≥ 4x + 2 Subtracting 4x from both sides: 5x ≥ 2 Dividing both sides by 5: x ≥ 2/5

a) 4(1 + x) > x - 2 Distributing the 4: 4 + 4x > x - 2 Subtracting x from both sides: 3x > -6 Dividing both sides by 3: x > -2

b) -(2x + 1) ≤ 3(x + 2) Distributing the negative sign: -2x - 1 ≤ 3x + 6 Adding 2x to both sides: -1 ≤ 5x + 6 Subtracting 6 from both sides: -7 ≤ 5x Dividing both sides by 5: -7/5 ≤ x

c) 6(2x - 1) - (2 + x) < 0 Distributing the 6: 12x - 6 - 2 -