Consider the following math sentence and find the answer(s).[br][math]x+5=8[/math]
How many answers did you find for this math sentence? What is the answer(s)? [br](what value of the variable x would make the equation true?)
One answer. Only one answer makes this math sentence true.[br][math]x=3[/math]
What steps did you take to find the answer [math]x=3[/math]?
Subtracted 5 on both sides
Describe the difference between the following two math sentences:[br][math]x+5=8[/math] and [math]x+5<8[/math]
They have a different symbol in between each side of the math sentence
An [i]equation[/i] is a type of math sentence where either side of the [i]equals [/i]sign must have the exact same value.[br]An [i]inequality[/i] is a type of math sentence where either side of the [i]inequality symbol (greater than, less than, greater than or equal to, less than or equal to)[/i].[br][br]The equations we have seen only have [i]one answer[/i].[br]The inequalities we will work with will have [i]infinite answers.[br][br][/i]We solve inequalities the same way we solve equations, using opposite operations.
[u]Greater than: (>)[/u][br][math]x>5[/math][br]x is greater than 5[br][br][u]Less than: (<)[/u][br][math]7<10[/math][br]7 is less than 10[br][br][u]Greater than or equal to: ([/u][math]>=[/math][u])[br][math]10>=10[/math][/u][br]10 is greater than or equal to 10[br][br][u]Less than or equal to: ([/u][math]<=[/math][u])[br][math]x<=3[/math][/u][br]x is less than or equal to 3
List 4 numbers that make the following inequalities true.[br][math]x>5[/math] (x is greater than 5)[br][br][math]x<=3[/math] (x is less than or equal to 8)
Is there any limit to the number of answers we can come up with?[br][br]Inequalities will have an infinite number of solutions where equations will normally only have one solution