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Samantha made a device that pours 300 ml of hot wax into molds. Due to a hardware flaw, the device pours 4 ml less than or more than 300 ml of wax into the molds.

The following absolute value equation can be used to determine the actual quantity of wax poured into the molds: [tex]|x-300|=4[/tex]

Here, [tex]x[/tex] represents the amount of wax, in ml, poured into the molds. Based on this information, what is the actual quantity of wax poured into the molds?

A. The actual quantity of wax poured into the molds is 1,200 ml or 304 ml.
B. The actual quantity of wax poured into the molds is 300 ml or 296 ml.
C. The actual quantity of wax poured into the molds is 4 ml or 296 ml.
D. The actual quantity of wax poured into the molds is 304 ml or 296 ml.

Sagot :

GinnyAnsweridn
To solve this problem, we need to work through the absolute value equation [tex]\( |x - 300| = 4 \)[/tex].

This equation means that the distance between [tex]\( x \)[/tex] and 300 on the number line is 4 units. To find the values of [tex]\( x \)[/tex] that satisfy this equation, we can split it into two separate cases:

1. [tex]\( x - 300 = 4 \)[/tex]
2. [tex]\( x - 300 = -4 \)[/tex]

Step-by-step solution:

1. Solve the first equation:
[tex]\[ x - 300 = 4 \][/tex]
To isolate [tex]\( x \)[/tex], add 300 to both sides of the equation:
[tex]\[ x = 300 + 4 \][/tex]
[tex]\[ x = 304 \][/tex]

2. Solve the second equation:
[tex]\[ x - 300 = -4 \][/tex]
To isolate [tex]\( x \)[/tex], add 300 to both sides of the equation:
[tex]\[ x = 300 - 4 \][/tex]
[tex]\[ x = 296 \][/tex]

The actual quantities of wax poured into the molds are 304 ml or 296 ml. Therefore, the correct answer is:

D. The actual quantity of wax poured into the molds is 304 ml or 296 ml.
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