You are watching: Justify each step of the solution
Starting indigenous the initial assumption that an equation has actually a solution, every simplification of the equation should have the very same solution set.
Explain each action in solving a simple equation as adhering to from the equality of number asserted in ~ the previous step, starting from the assumption that the original equation has actually a solution. Build a viable debate to justification a solution method.
Solve direct equations and inequalities in one variable, including equations with coefficients represented by letters.
A significant understanding in today"s class is the at any kind of step in fixing an equation the solution set should remain consistent. This requires students to slow-moving down and be an ext precise 보다 usual in their thinking (MP6). In slides 2 and also 3 of Solving and also Justifying Equations, college student verify what they had learned in a ahead lesson reflecting that a worth substituted in for the variable will make the equation true after ~ a term has actually been added to every side or each side has actually been multiplied by a non-zero constant.
(1) i will permit students to experiment with adding/subtracting a ax of their own choosing. I desire to repeat students the the term the is included or subtracted could be a variable. Also, ns remind students that the focus is not on isolating the variable, quite it is ~ above verifying the equivalence that the two expressions ~ manipulating every side that the equation.
(2) "Multiplying" by a non-zero constant could likewise mean multiply by a fraction with 1 in the molecule which would certainly be the exact same as dividing by the denominator of the fraction. You additionally have the alternative of an altering the statement above to main point or division by a non-zero consistent depending on the ax you select to use with your students.
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While students room working, ns will try to pinpoint a couple of students who determined to manipulate the problem in an interesting way. Ns then have actually a handful of students (3-5) placed their work-related on the board. I purposely pick various approaches together as adding variables, integers, subtracting integers, etc. (Adding two different integers will certainly not really present the variance in possibility).