Solve Equation (Absolute Value and Linear Inequalities)

Question

Solve Equation:

Topics are Absolute Value and Linear Inequalities. (Show complete solution)

 

1. | x+1 | ≤ | x-3 |

2. | x-6 | ≤ - 8

3. 1 - | 1/4x + 8 | > 3/4
4. [4x-2 < 8 or 3(x-1) < -2] and -2 ≤  5x ≤  10

Answer 1

1. x + 1 <= x - 3 has no solutions

   x + 1 <= 3 - x

   2x + 1 <= 3

   2x <= 2

    x <= 1

2. Absolute value of x - 6 <= -8 Has no solutions because absolute value is always greater than or equal to zero.

3. 1 - l (1/4)x + 8 l > 3/4

Subtract 3/4 from both sides & add | (1/4)x + 8 | to both sides we get:

1/4 > | (1/4)x + 8 |

-1/4 <  (1/4)x + 8  < 1/4

Subtract by 8

-33/4 < (1/4)x < -31/4

Multiply 4

-33 < x < -31