Question

A\5+3=-7 |x|+1=4 |x+1|=4

Answer 1

1)
|x|+1=4
IxI=3
x=+-3

2)
|x+1|=4
x+1=+-4
а)
x+1=-4
x₁=-5
б)
x+1=4
x₂=3
Ответ: x₁=-5, x₂=3

Answer 2

To solve these equations, let's break them down one by one:

1. $A\5+3=-7$

This equation appears to be written in an unusual way. If you meant to write $A \cdot 5 + 3 = -7$, then we can solve it as follows:

Subtract 3 from both sides:

$A \cdot 5 = -7 - 3$

$A \cdot 5 = -10$

Now, divide both sides by 5 to isolate A:

$A = -10/5$

$A = -2$

So, $A = -2$ is the solution to this equation.

2. $|x| + 1 = 4$

To solve for x in this equation, you can isolate |x| by subtracting 1 from both sides:

$|x| = 4 - 1$

$|x| = 3$

Now, you have two cases to consider since |x| can be either positive or negative:

a) $x = 3$ b) $x = -3$

So, there are two solutions: $x = 3$ and $x = -3$.

3. $|x + 1| = 4$

Similar to the previous equation, we'll isolate |x + 1| by subtracting 1 from both sides:

$|x + 1| = 4 - 1$

$|x + 1| = 3$

Now, again, you have two cases to consider:

a) $x + 1 = 3$

Subtract 1 from both sides:

$x = 3 - 1$

$x = 2$

b) $x + 1 = -3$

Subtract 1 from both sides:

$x = -3 - 1$

$x = -4$

So, there are two more solutions: $x = 2$ and $x = -4$.

In summary, for the three equations:

1. $A \cdot 5 + 3 = -7$ has one solution: $A = -2$.
2. $|x| + 1 = 4$ has two solutions: $x = 3$ and $x = -3$.
3. $|x + 1| = 4$ has two solutions: $x = 2$ and $x = -4$.