Question

A) x + |x| = 6 б) x - |x| = 5

Answer 1

Ответ:

a)x+|x|=6

x+x=6 , x>=0

x-x=6 , x<0

x=3 , x>=0

x=∅ , x<0

xЄ3

x=3

б)x-|x|=5

xЄ∅ , x>=0

x=5/2 , x<0

xЄ∅

xЄ∅

xЄ∅

Answer 2

Let's solve these two equations for the variable x:

A) x + |x| = 6

To solve this equation, we can consider two cases: one where x is non-negative (x ≥ 0) and one where x is negative (x < 0).

Case 1: x is non-negative (x ≥ 0): In this case, |x| is simply equal to x, so the equation becomes: x + x = 6 2x = 6 x = 6/2 x = 3

Case 2: x is negative (x < 0): In this case, |x| is equal to -x (because the absolute value of a negative number is its positive counterpart), so the equation becomes: x - (-x) = 6 x + x = 6 2x = 6 x = 6/2 x = 3

So, for both cases, the solution is x = 3.

B) x - |x| = 5

Again, let's consider two cases: one where x is non-negative (x ≥ 0) and one where x is negative (x < 0).

Case 1: x is non-negative (x ≥ 0): In this case, |x| is simply equal to x, so the equation becomes: x - x = 5 0 = 5

This case has no solution because it leads to an equation that is not true.

Case 2: x is negative (x < 0): In this case, |x| is equal to -x, so the equation becomes: x - (-x) = 5 x + x = 5 2x = 5 x = 5/2

So, for this case, the solution is x = 5/2.

Therefore, the second equation (B) has a solution only when x is negative, and in that case, x = 5/2. There is no solution for the non-negative case.