Lesson 7 Classification Of Solutions

Videos, examples, solutions to help Grade 8 students know the atmospheric condition for which a linear equation will have a unique solution, no solution, or infinitely many solutions.

New York State Common Core Math Grade 8, Module 4, Lesson vii

Common Core Math Course viii, Module 4, Lesson seven Worksheets (pdf)

Lesson seven Outcome

• Students know the weather condition for which a linear equation will accept a unique solution, no solution, or infinitely many solutions.

Lesson 7 Summary

• There are three classifications of solutions to linear equations: one solution (unique solution), no solution, or infinitely many solutions.

Equations with no solution will, subsequently being simplified, accept coefficients of x that are the aforementioned on both sides of the equal sign and constants that are different. For example, ten + b = 10 + c, where b, c are constants that are not equal. A numeric example is 8x + 5 = 8x - 3.

Equations with infinitely many solutions volition, afterward beingness simplified, have coefficients of 10 and constants that are the same on both sides of the equal sign. For example, x + a = ten + a, where a is a constant. A numeric example is 6x + i = i + 6x.

NYS Math Module 4 Grade 8 Lesson 7 Classwork

Exercises 1–3
Solve each of the following equations for x.

7x - iii = 5x + 5
7x - 3 = 7x + 5
7x - 3 = -3 + 7x
Notation: if the coefficients of ten are different and the value of the constants are the same, the only solution is ten = 0. For instance, 2x + 12 = x + 12

Bear witness Pace-by-pace Solutions

Exercises ane–3

Activity: What can we see in an equation that will tell usa well-nigh the solution to the equation?

Exercises four–ten
Give a brief explanation as to what kind of solution(s) yous wait the following linear equations to have. Transform the equation into a simpler form if necessary.

11x - 2x + xv = 8 + 7 + 9x
iii(ten -14) + 1 = -4x + 5
-3x + 32 - 7x = -2(5x + 10)
1/two(8x + 26) = thirteen + 4x
Write two equations that have no solutions.
Write two equations that have i unique solution each.
Write two equations that take infinitely many solutions.

Prove Step-by-footstep Solutions

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