Question

plz answer my question correctly I will mark you as BRAINLIEST.....!!
plz answer these I will thank all your answers​

Answer 1

$5.) \: \: |x - 1| + |x - 3| = 6 \\ x + 1 + x + 3 = 6 \\ 2x + 4 = 6 \\ 2x = 6 - 4 \\ 2x = 2 \\ x = \frac{2}{2} \\ x = 1$

$6.) \: \: | | |x - 1| - 1| - 1| = 1 \\ | |x - 1| - 1 | + 1 = 1 \\ |x - 1| + 1 + 1 = 1 \\ x + 1 + 1 + 1 = 1 \\ x + 3 = 1 \\ x = - 4$

Hope it helps you.

Please mark it as Brainliest and follow me!!!!

Answer 2

The person above me didn't solve correctly.

Q.5

We must be careful because an absolute value gives two values. We must separate into two possibilities, where the absolute is positive, 0 or negative.

1. x≥3 (Where both are positive)

→ x-1+x-3=6 → 2x-4=6 → x=5 is the solution.

2. 1≤x<3 (Where x-1≥0, x-3<0)

→ x-1-x+3=6 → 2=6 is falsehood. → There is no solution.

3. x<1 (Where both are negative)

→ -x+1-x+3=6 → -2x+4=6 → x=-1 is the solution.

Q.5 All the solutions are x=5 or x=-1.

Q.6

If the absolute value of a number is one, what is the number? It should be either 1 or -1. → ||x-1|-1| is either 0 or 2.(Two cases)

1. Where ||x-1|-1|=0

→ |x-1|-1=0 → |x-1|=1 → x=2 or x=0

2. Where ||x-1|-1|=2

→ |x-1|-1=±2 → |x-1| should be 3 because the absolute value is not negative.

→ x=4

Q.6 All the solutions are x=0, x=2 or x=4.