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Zorluk: ZorSolving One-Variable Linear Equations

A network engineer is configuring a load balancer to distribute traffic across two servers. The equation below models the traffic distribution, where tt represents the number of active connections:

5(2t−4)−3t=4(t+2)−(t−8)5(2t - 4) - 3t = 4(t + 2) - (t - 8)

Calculate the required number of active connections, tt, to successfully balance the server loads.

Cevap: 9 connections

Cevap

9
By successfully applying the distributive property on both sides, combining the variable and constant terms, and isolating the variable, the equation perfectly balances when the variable is exactly 9.

Adım Adım Çözüm

1
Distribute the coefficients and negative signs across the parentheses on both sides of the equation.
10t−20−3t=4t+8−t+810t - 20 - 3t = 4t + 8 - t + 8
Distribution removes the parentheses, allowing individual terms to be combined.
2
Combine like terms on each side of the equation.
7t−20=3t+167t - 20 = 3t + 16
Simplifying each side individually makes it easier to balance the equation.
3
Subtract 3t3t from both sides of the equation.
4t−20=164t - 20 = 16
This groups all the variable terms on one side of the equation.
4
Add 20 to both sides and divide by 4.
4t=36  ⟹  t=94t = 36 \implies t = 9
Isolating the variable determines the final numerical solution.

Anahtar Kavram

Solving multi-step linear equations involving the distributive property and combining like terms.
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Konular

Solving One-Variable Linear Equations

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