Question

Б) |18-x|=3,24 в) |3x+9|=-6 г)|0,01-0,02|=0

Answer 1

Б) х=14.76
в) х=-5
г) х=0,01

Answer 2

To solve each of these absolute value equations, we need to consider both the positive and negative cases for the expression inside the absolute value. Let's solve each equation step by step:

a) |18 - x| = 3.24

Positive case: 18 - x = 3.24 Subtract 18 from both sides: -x = 3.24 - 18 -x = -14.76 Multiply both sides by -1 (to get x alone): x = 14.76

Negative case: -(18 - x) = 3.24 Multiply -1 inside the parentheses: -18 + x = 3.24 Add 18 to both sides: x = 3.24 + 18 x = 21.24

So the solutions for this equation are x = 14.76 and x = 21.24.

b) |3x + 9| = -6

Since an absolute value can never be negative, this equation has no real solutions. There are no values of x that will satisfy this equation.

c) |0.01 - 0.02| = 0

Positive case: 0.01 - 0.02 = 0 Subtract 0.02 from 0.01: -0.01 = 0 This is not true.

Negative case: -(0.01 - 0.02) = 0 Multiply -1 inside the parentheses: -0.01 + 0.02 = 0 0.01 = 0 This is also not true.

Since neither the positive nor the negative case resulted in a true statement, this equation also has no real solutions. The absolute value of the expression is always positive, so it can never equal zero.

To summarize:

a) The solutions for |18 - x| = 3.24 are x = 14.76 and x = 21.24. b) There are no real solutions for |3x + 9| = -6. c) There are no real solutions for |0.01 - 0.02| = 0.