Answer
a) $x + 2= 3$ and $x +2 = -3$
b) $1$ and $-5$
c) By isolating absolute value equation into linear equations
Work Step by Step
a) The equation | x+2|=3 can be isolated into two linear equations where the right side value will take a positive value and negative value. Hence the value of $x + 2$ can be $3$ or $-3$.
Equating $x+2$ to $3$, we get the linear equation $x + 2 = 3$. Similarly , when we equate to $ -3$, we get the linear equation $x + 2 = -3$.
b) Solving $x + 2 = 3$
subtracting $2$ from both sides of the equation,
$x = 1$
solving $x + 2 = -3$
subtracting $2$ from both sides of the equation,
$x = -5$
hence, $x = 1$ and $x = -5$ are the solutions.
c) As seen in part a) and b), the absolute value equation was first isolated to two linear equations which was then solved to derive the values of $x$. This way linear equations help solve absolute value equations
