A technician is testing two different electrical circuits. The voltage in Circuit A is giv… — Armed Services Vocational Aptitude Battery (ASVAB)

A technician is testing two different electrical circuits. The voltage in Circuit A is given by the expression $5v - 12$ , where $v$ is a variable setting on the power supply. The voltage in Circuit B is given by $2(v + 9)$ . Both circuits are adjusted to have the exact same voltage. Fill in the blanks with the correct numerical values.

Answer:The required setting

v

is 【10】 and the resulting voltage is 【38】.

Answer

The setting

v

is 10 and the resulting voltage is 38.

By setting the two expressions equal, expanding the parentheses, and systematically isolating

v

, we find the setting must be 10. Plugging 10 back into the expression evaluates the voltage to 38 for both circuits.

Step-by-Step Solution

Set the expressions for Circuit A and Circuit B equal to each other.

5v - 12 = 2(v + 9)

The problem states that both circuits are adjusted to have the exact same voltage.

Distribute the 2 on the right side of the equation.

5v - 12 = 2v + 18

The distributive property is required to eliminate parentheses and expose the variable term.

Subtract

2v

from both sides of the equation.

3v - 12 = 18

To consolidate all variable terms on one side of the equation.

Add 12 to both sides of the equation.

3v = 30

To isolate the variable term by moving constants to the other side.

Divide both sides by 3.

v = 10

To solve for the variable

v

Substitute

v = 10

back into either original expression.

5(10) - 12 = 50 - 12 = 38

To find the resulting voltage as requested by the second blank.

Key Concept

Solving linear equations with variables on both sides and distributive property

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