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Chapter 8: Q. 316 (page 982)

In the following exercises, solve.

3t-6=1t

Short Answer

Expert verified

The solution of the equation 3t-6=1tis

t=-3

Step by step solution

01

Step 1. Given information  

The given equation is

3t-6=1t

02

Step 2. Solution of equation  

Terms of the equation are not defined for t=6&t=0

sorole="math" localid="1647800509525" 3t-6=1t,t鈮�6,t鈮�0

The least common denominator of all denominators in the equation ist(t-6)

multiply both sides of the equation by the least common denominator t(t-6)

role="math" localid="1647800645888" t(t-6)3t-6=t(t-6)1tt3=(t-6)13t=t-6t=-3

So the solution of the equation is role="math" localid="1647800631368" t=-3

03

Step 3. Verification 

Substitute t=-3in the equation

3t-6=1t3-3-6=?1-33-9=?1-31-3=1-3

The left-hand side is equal to the right-hand side so the solution is correct.

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