# Video: US-SAT03S3-Q17-735143965978

What is the value of π that satisfies the equation 3(π β 3) + 7(2π + 1) = 11π?

04:06

### Video Transcript

What is the value of π that satisfies the equation three times π minus three plus seven times two π plus one equals 11π?

First, weβll copy down the equation. And then, weβll need to distribute this multiplied by three and multiplied by seven across the parentheses. Weβll start with our three. Three times π equals three π. Three times negative three equals negative nine. And then, we have seven times two π which equals 14π. And seven times one will equal seven. And weβll bring down the 11π. At this stage, we want to combine like terms.

Three π and 14π are like terms. And that means we can add them together. Positive three π plus 14π equals 17π. Negative nine and positive seven are also like terms. Theyβre numbers without a variable. And so, we can add them together. Negative nine plus seven equals negative two. 17π minus two equals 11π. At this point, we want to get our terms with the variable π onto the same side of the equation. We can do this in one of two ways.

We can subtract 11π from both sides of the equation. 17π minus 11π gives us six π. And 11π minus 11π gives us zero. If we subtracted 11π from both sides, we would get six π minus two equals zero. We can also solve by subtracting 17π from both sides. 17π minus two minus 17π equals negative two. And 11π minus 17π equals negative six π. We would have negative two equals negative six π or we would have six π minus two equals zero.

On the left equation, we would divide both sides by negative six to get our π by itself. Negative six π divided by negative six equals π. And negative two over negative six is the same thing as positive two over six, which can be simplified to one-third. Or on the right side, to get π by itself, we add two to both sides. And we have six π equals two. To get π by itself, we divide both sides by six. And then, we have π equals two over six, which we simplified to one-third. π equals one-third.

If we wanted to check, we can take one-third and plug it back in for π. One-third minus three is one-third minus nine-thirds. Three written as a fraction of three is nine-thirds. One-third minus nine-thirds is negative eight-thirds. And if we want to multiply that by three, we get negative twenty-four thirds. Two times one-third equals two-thirds plus one. We can write one as three over three. Two-thirds plus three-thirds equals five-thirds. And we multiply that by seven which gives thirty-five thirds. And 11 times one-third equals eleven-thirds. Since all three of our fractions have a denominator of three, we add negative 24 and positive 35. And it becomes a fraction over three. Negative 24 plus 35 equals 11. And that means π equals one-third does satisfy this equation.