Question

|x + 3| + |x - 1| = 4​

Answer 1

2х-1=4-3
х=1
|1+3|+|1-1|=4

Answer 2

2х-1=4-3

х=1

|1+3|+|1-1|=4

Answer 3

To solve the equation |x + 3| + |x - 1| = 4, you need to consider different cases based on the sign of the expressions inside the absolute value bars.

Case 1: x + 3 is non-negative, and x - 1 is non-negative. In this case, you have two absolute values without negation, so the equation becomes:

x + 3 + x - 1 = 4

Combine like terms:

2x + 2 = 4

Subtract 2 from both sides:

2x = 4 - 2 2x = 2

Divide by 2:

x = 1

Case 2: x + 3 is non-negative, and x - 1 is negative. In this case, you have:

x + 3 - (x - 1) = 4

Simplify:

x + 3 - x + 1 = 4

Combine like terms:

4 = 4

This equation is always true, so it doesn't provide any new solutions.

Case 3: x + 3 is negative, and x - 1 is non-negative. In this case, you have:

-(x + 3) + (x - 1) = 4

Simplify:

-x - 3 + x - 1 = 4

Combine like terms:

-4 = 4

This equation is never true, so it doesn't provide any solutions.

Case 4: x + 3 is negative, and x - 1 is negative. In this case, you have two absolute values with negation, so the equation becomes:

-(x + 3) - (x - 1) = 4

Simplify:

-x - 3 - x + 1 = 4

Combine like terms:

-2x - 2 = 4

Add 2 to both sides:

-2x = 4 + 2 -2x = 6

Divide by -2:

x = -3

So, there are two solutions to the equation |x + 3| + |x - 1| = 4:

x = 1 (from Case 1) x = -3 (from Case 4)