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Zorluk: OrtaSolving One-Variable Linear Equations

A technician is testing two different electrical circuits. The voltage in Circuit A is given by the expression 5v−125v - 12, where vv is a variable setting on the power supply. The voltage in Circuit B is given by 2(v+9)2(v + 9). Both circuits are adjusted to have the exact same voltage. Fill in the blanks with the correct numerical values.

Cevap:The required setting vv is 【10】 and the resulting voltage is 【38】.

Cevap

The setting vv is 10 and the resulting voltage is 38.
By setting the two expressions equal, expanding the parentheses, and systematically isolating vv, we find the setting must be 10. Plugging 10 back into the expression evaluates the voltage to 38 for both circuits.

Adım Adım Çözüm

1
Set the expressions for Circuit A and Circuit B equal to each other.
5v−12=2(v+9)5v - 12 = 2(v + 9)
The problem states that both circuits are adjusted to have the exact same voltage.
2
Distribute the 2 on the right side of the equation.
5v−12=2v+185v - 12 = 2v + 18
The distributive property is required to eliminate parentheses and expose the variable term.
3
Subtract 2v2v from both sides of the equation.
3v−12=183v - 12 = 18
To consolidate all variable terms on one side of the equation.
4
Add 12 to both sides of the equation.
3v=303v = 30
To isolate the variable term by moving constants to the other side.
5
Divide both sides by 3.
v=10v = 10
To solve for the variable vv.
6
Substitute v=10v = 10 back into either original expression.
5(10)−12=50−12=385(10) - 12 = 50 - 12 = 38
To find the resulting voltage as requested by the second blank.

Anahtar Kavram

Solving linear equations with variables on both sides and distributive property
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Konular

Solving One-Variable Linear Equations

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