You Try! A machine prints trading cards and then trims them to the correct size. The absolute value equation |w - 3.5|= 0.003 gives the width, in inches, allowed for the cards to be certified authentic. What are the allowed widths, w, according to the equation?
( 3.503) and ( 3.497)
The allowed widths, w, according to the equation |w - 3.5| = 0.003 are 3.503 and 3.497.
To solve the absolute value equation |w - 3.5| = 0.003, we can set up two separate equations by considering the positive and negative cases of the absolute value:
For the positive case: w - 3.5 = 0.003
Adding 3.5 to both sides: w = 3.503
For the negative case: -(w - 3.5) = 0.003
Distributing the negative sign: -w + 3.5 = 0.003
Subtracting 3.5 from both sides: -w = -3.497
Multiplying both sides by -1 (to get w by itself): w = 3.497
So, the allowed widths, w, according to the absolute value equation, are 3.503 and 3.497 inches.
To find the allowed widths, we need to solve the absolute value equation |w - 3.5| = 0.003.
Step 1: Set up two equations.
a) w - 3.5 = 0.003
b) -(w - 3.5) = 0.003
Step 2: Solve for w in each equation.
a) w - 3.5 = 0.003
Add 3.5 to both sides:
w = 0.003 + 3.5
w = 3.503
b) -(w - 3.5) = 0.003
Distribute the negative sign:
-w + 3.5 = 0.003
Substract 3.5 from both sides:
-w = 0.003 - 3.5
-w = -3.497
Multiply both sides by -1 to isolate w:
w = -(-3.497)
w = 3.497
So the allowed widths, w, according to the equation |w - 3.5| = 0.003, are 3.503 and 3.497 inches.