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# Solving and graphing linear inequalities

## Video transcript

whereas to represent the inequality Y is greater than five on a number line and on the coordinate plane so let's do the number line first let me just draw out a number line that's my number line all the possible values of Y let's make that zero on the number line we could obviously go into the negative into negative numbers but we're going to be greater than five so I'll focus on the positive side so let's say that's one two three four five one two three four five and then that's six seven so forth and so on y is and this number line represents Y and Y is going to be greater than five not greater than or equal to so we're not going to be eating to be including five in the numbers that can be Y so we're not going to include five so we're going to do an open circle around five and all of the other values greater than five will be included so if there was a greater than or equal to sign we would have filled it in but since it's just greater than we're not including the five so that's we've represented it on the number line so let's do the same thing on the coordinate plane let me draw coordinate plane here and just using the standard convention that is my y-axis right there and then the horizontal axis I'll just assume is my x-axis is my x-axis and let me draw some Y values positive Y values one two three four five that is five right there and you go six seven you can just keep going into larger and larger numbers and we want Y to be greater than five so it's not going to be greater than or equal to so we're not going to include five so at five at Y is equal to five we will draw a dotted line that shows that we're not including that shows that we are not including Y is equal to five but we want to include all of the other values greater than five so that we will shade in so here we have shaded in all of the values greater than five it was greater than or equal to five we would have drawn a bold line over here so no matter what X is no matter what X we pick Y is going to be greater than five five