Question

25 POINTS

Answer 1

Answer:

False

Step-by-step explanation:

Equations With Absolute Value

The absolute value of any number is defined as

$|x|=\left \{ {{x,\ x\geq 0} \atop {-x,\ x< 0}} \right.$

To solve any equation where the absolute value bars appear, we must consider both signs of its argument because it can be positive or negative.

The equation is given as

$7- |4x+1| =-2$

To solve it, we must isolate the absolute value and then (not before), consider both signs for its argument.

The proposed procedure consist in writing the equation as two separate equations:

$7-4x+1=-2$

$7-4x+1=2$

which is wrong because we are changing the sign of the right side of the equation without isolating the absolute value. Those equations would lead to inaccurate answers. So the statement is FALSE

The correct procedure is first to isolate the absolute value

$7+2 = |4x+1|=9$

Now we set

$4x+1=9\\or\\4x+1=-9$

which lead to the solutions

x = 2, x = - 5/2