Math

QuestionSolve the equation 2(2t5)=202t2(2t-5)=20-2t. What is the solution set? A. (Enter integer or fraction) B. All real numbers C. Empty set.

Studdy Solution

STEP 1

Assumptions1. The given equation is (t5)=20t(t-5)=20-t . We are looking for the solution set, which is the set of all values of tt that satisfy the equation

STEP 2

First, we need to simplify the equation. We can do this by distributing the 22 on the left side of the equation.
2(2t5)=4t102(2t-5) =4t -10So, the equation becomes4t10=202t4t -10 =20 -2t

STEP 3

Next, we need to get all terms involving tt on one side of the equation and the constants on the other side. We can do this by adding 2t2t to both sides of the equation.
t10+2t=202t+2tt -10 +2t =20 -2t +2tThis simplifies to6t10=206t -10 =20

STEP 4

Next, we add 1010 to both sides of the equation to isolate the term with tt on one side.
6t10+10=20+106t -10 +10 =20 +10This simplifies to6t=306t =30

STEP 5

Finally, we divide both sides of the equation by $$ to solve for $t$.
t=30t = \frac{30}{}

STEP 6

Calculate the value of tt.
t=306=5t = \frac{30}{6} =5The solution set is {5}\{5\}.

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