Video Transcript
Solve the inequality nine ๐ฆ is greater than 77 plus two ๐ฆ.
When our instructions tell us to solve the following inequality, what theyโre asking us to do is find the values for ๐ฆ that make the statement true. To do that, weโll need to isolate ๐ฆ. Right now, we have a ๐ฆ on both sides of our inequality. Before we can isolate ๐ฆ, weโll need to get both of these variables onto the same side of the equation.
We can do that by subtracting two ๐ฆ from both sides of our inequality. Nine ๐ฆ minus two ๐ฆ equals seven ๐ฆ. Bring down our inequality symbol. Bring down the 77. Two ๐ฆ minus two ๐ฆ equals zero. So thereโs nothing to bring down there. In this line, seven is being multiplied by ๐ฆ. But we want ๐ฆ by itself. So we can divide seven ๐ฆ by seven and also 77 by seven. Seven ๐ฆ divided by seven equals ๐ฆ. Bring down our inequality symbol. 77 divided by seven equals 11.
This is our solution to the inequality. Nine is greater than eleven. Any time we plug in something larger than eleven for ๐ฆ in this inequality, this statement will be true. ๐ฆ is greater than eleven.