Choose the two equations you would use to solve the absolute value equation below. Then solve the two equations.

\[|x + 5| = 55\]

∣ x + 5∣ = 55 x + 5 = 55 ∨ x + 5 = − 55 x = 55 − 5 ∨ x = − 55 − 5 x = 50 ∨ x = − 60

Answered by Anonymous | 2024-06-10

To solve |x + 5| = 55, we consider two cases based on whether x + 5 is positive or negative, leading to x = 50 and x = -60 as solutions.
To solve the absolute value equation |x + 5| = 55, we begin by understanding that the absolute value of a number is the distance of that number from zero on the number line, irrespective of the direction. This means we can have two cases for the contents of the absolute value to be equal to 55.
Case 1: Positive Value
If x + 5 is positive, we can drop the absolute value bars without changing the sign:
x + 5 = 55
Now, subtract 5 from both sides to solve for x:
x = 55 - 5
x = 50
Case 2: Negative Value
If x + 5 is negative, the absolute value of that expression is equal to the negative of the expression itself:
-(x + 5) = 55
Multiply both sides by -1 to get rid of the negative sign:
x + 5 = -55
Subtract 5 from both sides to solve for x:
x = -55 - 5
x = -60
The two solutions for the equation are x = 50 and x = -60.

Answered by AakanshaB | 2024-06-25

The absolute value equation ∣ x + 5∣ = 55 can be solved by creating two equations: x + 5 = 55 and x + 5 = − 55 . Solving these gives the results x = 50 and x = − 60 . Therefore, the solutions are x = 50 and x = − 60 .
;

Answered by Anonymous | 2024-09-04