BELLWORK Evaluate each expression if x= -4 and y= -9

FRIDAY’S CLASSWORK ANSWERS

EVALUATE EXPRESSIONS INVOLVING ABSOLUTE VALUE SOLVE ABSOLUTE VALUE EQUATIONS SOLVING ABSOLUTE VALUE EQUATIONS 1-4

ABSOLUTE VALUE EXPRESSIONS The absolute value of a number is it’s distance from 0 on the number line The absolute value of a number is always positive Symbols: |a|= a when a > 0 and |-a|=a when a <0 *Remember: It is the distance from 0 on the number line and a distance is NEVER negative*

SOLVING ABSOLUTE VALUE EQUATIONS When solving absolute value equations we must always look at two cases: a= b and a= -b When we solve absolute value equations we can have three types of solutions: ~Two Solutions ~One solution ~ No Solutions

WHY Lets look at |x|=3 We know that if x=3 then |3|=3. However, x can also be -3. We still get that |-3|=3 So we must make sure to take both cases, x=3 and x=-3

ALWAYS CHECK YOUR SOLUTIONS!! TO ABSOLUTE VALUE EQUATIONS

TWO SOLUTIONS: I DO Example: Solve. Check your solutions. |y+3|=8 Check!!

TWO SOLUTIONS: WE DO Example: Solve. Check your solutions. 9=|x+12| Check!!

TWO SOLUTIONS: YOU DO Example: Solve. Check your solutions. 8=|y+5| Check!!

IS THIS POSSIBLE? Is it possible to have an absolute value equation that looks like this?: |x|= -10 Why not? The absolute value of a number is always positive! (remember we are talking about a distance)

SO WHAT HAPPENS? Also called an empty set.

I DO Example: Solve. Check your solutions. |6-4t|+5=0

WE DO:

BELLWORK: Example: Solve. Check your solutions. -2|3a|=6

HOMEWORK ANSWERS 15.) ) ) ) ) {34, -8} 25.) {4,-14} 27.) {-2,-10}

A FEW THINGS TO REMEMBER Always make sure the absolute value is isolated on one side of the equation. Split the problem into two cases, a = b and a = -b If, after isolating the Absolute Value, we have a situation where the absolute value equals a negative, stop! The answer is no solution. Always check your work!!!

WHY IT IS IMPORTANT TO CHECK YOUR ANSWERS: Sometimes in mathematics, we do all this work to obtain an answer that just doesn’t work out These are called extraneous solutions These extraneous solutions are not actual answers, we find this out when we check our work

I DO Remember: We must look at two different cases Check!!

WE DO Remember: We must look at two different cases Check!!

YOU DO Remember: We must look at two different cases Check!!

HOMEWORK TB pg (#28-34 all)