Question

|x|-4=1,2​

Answer 1

$|x| - 4 = 1.2 \\ |x| = 1.2 + 4 \\ |x| = 5.2 \\ x_1 = 5.2 \\ x_2 = - 5.2$

$3 |x| - 4 = 5 \\ 3 |x| = 5 + 4 \\ 3 |x| = 9 \\ |x| = 3 \\ x_1 = 3 \\ x_2 = - 3$

Answer 2

To solve the equation |x| - 4 = 1/2, we can break it down into two separate cases based on the absolute value.

Case 1: x is positive or zero (x ≥ 0) In this case, |x| simplifies to x, so the equation becomes: x - 4 = 1/2

We can solve for x by adding 4 to both sides: x - 4 + 4 = 1/2 + 4 x = 1/2 + 4 x = 9/2

So, one solution in this case is x = 9/2.

Case 2: x is negative (x < 0) In this case, |x| simplifies to -x (since we are dealing with a negative value), so the equation becomes: -x - 4 = 1/2

We can solve for x by adding 4 to both sides and multiplying by -1: -x - 4 + 4 = 1/2 + 4 -x = 1/2 + 4 -x = 9/2

Now, we multiply both sides by -1 to isolate x: x = -9/2

So, another solution in this case is x = -9/2.

Therefore, the solutions to the equation |x| - 4 = 1/2 are x = 9/2 and x = -9/2.