Question

1)x+4|=|x-7| 2)|x+1|=|x-9|

Answer 1

|х+4|=|х-7|
x+4=x-7
x+4=-(x-7)
x=3/2
x=1.5

|x+1|=|x-9|
x+1=x-9
x+1=-(x-9)
x=4

Answer 2

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

1. $|x+4| = |x-7|$

To solve this equation, we consider two cases:

Case 1: $x+4 = x-7$ $x+4 - x + 7 = 0$ $11 = 0$ (No solution)

Case 2: $x+4 = -(x-7)$ $x+4 = -x + 7$ $2x = 3$ $x = \frac{3}{2}$

So, the solution to the equation is $x = \frac{3}{2}$.

2. $|x+1| = |x-9|$

Again, let's consider two cases:

Case 1: $x+1 = x-9$ $x+1 - x + 9 = 0$ $10 = 0$ (No solution)

Case 2: $x+1 = -(x-9)$ $x+1 = -x + 9$ $2x = 8$ $x = 4$

So, the solution to the equation is $x = 4$.

To summarize:

1. $x = \frac{3}{2}$

2. $x = 4$