Solving Absolute Value Equations
Grab a warm-up from the wooden desk
Solve. Crumple. Toss!
Goals:
Warm-up #1
Solve the equations below. Show all your work. Check your solution.
Warm-up #2
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.
Three function families of Algebra 1
Linear Exponential Quadratic
Recall: What does absolute value mean?
Linear absolute Value Equations can have 0, 1, or 2 possible solutions!
|x|=8 | |n+2|=3 | |x-4|=6 |
Now check it! | Now check it! | Now check it! |
Math is about efficiency. How can you solve bigger linear absolute value equations more efficiently?
|3x+1|=-5 | |3x+9|-10=-4 | |x-2|+5=9 |
Now check it! | Now check it! | Now check it! |
|2x-3|+6=9 | |3+x|=-3 | -2|5x-1|-3=-11 |
Now check it! | Now check it! | Now check it! |
An ____________________ solution is an apparent solution that must be rejected because it does not satisfy the original equation.
|2x+12|=4x | |3x-4|=|x| | |x+5|=|x+11| |
Now check it! | Now check it! | Now check it! |
Complete the statement:
When solving linear absolute value equations it’s important to pay attention to… because…
Mobile Puzzles
Complete the problem. Show all your work!
Correct answers
Resources
Mod 2 Standards (needs updated)
�S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.�A. Focus on polynomial expressions that simplify to forms that are linear or quadratic.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.�A. Focus on applying linear and simple exponential expressions
A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations and inequalities arising from linear, quadratic, simple rational, and exponential functions.�A. Focus on applying linear and simple exponential expressions.
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3 Solve linear equations and inequalities in one variable
A.CED.4 Rearrange Formulas to highlight a quantity of interest, using the same reasoning as in solving equations.�A. Focus on formulas in which the variable of interest is linear or square. For example, rearrange Ohm’s law V-IR to highlight resistance R, or rearrange the formula for the area of a circle A=pir^2 to highlight radius r.
S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
Warm-up #2
Using the digits 1 to 9 at most once each, fill in the boxes to make a true statement.