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Solve for the unknown, and then check your solution.$$2+3(5 t-9)=7 t-3(9-3 t)$$

$$2$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

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Idaho State University

Lectures

00:34

Solve the equation.$$7…

01:37

Solve the equation.$$<…

01:01

02:32

Solve the equations by fir…

01:00

Solve $t(t+3)-t(t-5)=4(t-5…

02:06

Solve.$9 t(t+2)-3 t(t-…

01:59

Solve.$$2(t-5)-3(2…

00:41

Solve each equation and ch…

right for this linear equation, We're going to solve the following two plus three times in parentheses. Five T minus nine is equal to seven times T minus three times in parentheses, nine minus three t. So this is a linear equation because the T value, which is the unknown that we're looking for, is raised to the power of one. And both of these expressions should equal each other. And we're gonna use the fact that addition and subtraction will under each other and same thing, multiplication and division will under each other. So first thing there to do simplify this. We can do this by distributing on the left side of the equation the three unto the unto, this little parentheses and then on the right side, distributing the negative three onto this parentheses. So it's gonna be three times five t and also three times negative night on the on the right side, Obi Negative. Three times nine and negative. Three times negative. Three t. So Well, that's what we're gonna have to two plus and then distributed. Three. So three times five Teen, that's 15 T minus three times nine, which is 27. This is negative because the negative nine we're here. So this is negative. 27. And on the right side will be 17 distributed three into each value. Inside the parentheses, we're going to have negative three times nine. That's negative. 27 and also negative. Three times negative three t is gonna be plus 19. So the negatives cancel each other out. Right now, we can simplify this further down by adding, like values. So we have to and negative 27 that can be at it. And on the right side, we have 17 in 19 that can be added together. So to minus 27 is negative. 25. We're gonna have 15 teen minus 25. Then on the right side, we're gonna have 17 plus 90 which is 16 t minus 27. Now, what we want to do with this is we want to get the 15 t to the right side of the equation and the negative 27 to the left side of the equation. And we're gonna do this by subtracting both sides of the equation with negative 15. So we're gonna have 15 T minus 25 minus 15 t and on the right. So we're gonna do the same thing. 16, 2 minutes. 27 minus 15 t Now the 15 t's cancel each other out. So we're left with negative 25 on the left side. And we have 16 to minus 15. T is just one times t. So just tea. No, we're left with this. So right here, we're gonna add 27 negative 27 to both sides of the equation in order to get t by itself. So we're gonna have t minus 27 plus 27 negative. 25 plus 27. So we're gonna be left. Would the 27th and the rights. I can cancel each other out. And we have 27 minus 25 which is just to is equal to t. We could rearrange that, and it's the same thing. T is equal to two, so we can quickly check by plugging in, Um, by replacing T with two. Until the original equation which waas two plus three, we have five times two. So we replaced the tea with two minus nine. That's equal to seven times T, which is just seven times two. My next three and then our parent to seize nine minus three times T, which is three times to. So we could just plug all of these values into a calculator and you should have the expression five equals five, which again it's true. So therefore, t equals to this. Our answer.

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