Question

8 write an equation that has the given number of solutions.
a. no solution
b. infinitely many solutions
math journal write a one - variable linear equation that has infinitely many solutions. then change one term in your equation so that it has no solution. how do you know that each of your equations has the correct number of solutions?
of lesson checklist
eractive glossary find the entry for linear equation. give 3 examples of
equations.
check go back to the unit 3 opener and see what you can check off.
determine the number of solutions to one - variable equations

Explanation:

Step1: Write no-solution equation

A no-solution linear equation has equal coefficients for the variable but unequal constants. Example: $2x + 3 = 2x + 5$. Simplify: $3 = 5$ (false, no solution).

Step2: Write infinite-solutions equation

An infinite-solutions linear equation has equal coefficients and constants. Example: $3x - 4 = 3x - 4$. Simplify: $-4 = -4$ (true for all $x$).

Step3: Math Journal example

Infinite-solutions equation: $4x + 2 = 4x + 2$. Change constant term: $4x + 2 = 4x + 6$ (no solution). Check: Simplify to $2=6$ (false, no solution) vs original $2=2$ (true, infinite).

Answer:

a. $2x + 3 = 2x + 5$
b. $3x - 4 = 3x - 4$
Math Journal: Infinite-solutions: $4x + 2 = 4x + 2$; No-solution: $4x + 2 = 4x + 6$ (changed constant term). We know by simplifying: equal variable coefficients + unequal constants = no solution; equal coefficients + equal constants = infinite solutions.