Calee Leger - 8th Grade Math
email: [email protected]
11/04-11/07
Solving Linear Equations in One Variable
Unit 3 Lesson 11
8.EE.C.7 Solve linear equations in one variable
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the for x=a, a=a, or a=b (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whole solutions require expanding expressions using the distributive property and collecting like terms.
In this cluster, the terms students should learn to use with increasing precision are intersecting, parallel lines, coefficient, distributive property, like terms, substitution, and system of linear equations.
As students transform linear equations in one variable into simpler forms, they discover the equations can have one solution, infinitely many solutions, or no solution. When the equation has one solution, the variable has one value that makes the equation true as in 12-4y=16. The only value for that makes this equation true is -1.
When the equation has infinitely many solutions, the equation is true for all real numbers as in 7x+14=7(x+2). As this equation is simplified, the variable terms cancel leaving 14=14 or 0=0. Since the expressions are equivalent, the value for the two sides of the equation will be the same regardless which real number is used for the substitution.
When an equation has no solutions, it is also called an inconsistent equation. This is the case when the two expressions are not equivalent as in 5x-2=5(x+1). When simplifying this equation, students will find that the solution appears to be two numbers that are not equal, -2 does not equal 1. In this case, regardless which real number is used for the substitution, the equation is not true and therefore has no solution.
Vocabulary to Review: coefficient, distributive property, like terms, perimeter, term, variable.