IM 8.4.7 Lesson: All, Some, or No Solutions

Which one doesn’t belong?

[list=1][*][math]5+7=7+5[/math] [/*][*][math]5\cdot7=7\cdot5[/math][/*][*][math]2=7-5[/math][br][/*][*][math]5-7=7-5[/math][br][/*][/list][br]Explain your reasoning.

Select all the equations that are true for [i]all[/i] values.

[math]2t+6=2(t+3)[/math] [math]5-9+3x=-10+6+3x[/math] [math]\frac{1}{2}+x=\frac{1}{3}+x[/math] [math]\frac{1}{4}(20d+4)=5d[/math] [math]y\cdot-6\cdot-3=2\cdot y\cdot9[/math] [math]v+2=v-2[/math] [math]n=n[/math] [math]3(n+1)=3n+1[/math]

Select all the equations that are true for [i]no[/i] values.[br]

[math]y\cdot-6\cdot-3=2\cdot y\cdot9[/math] [math]\frac{1}{4}(20d+4)=5d[/math] [math]2t+6=2(t+3)[/math] [math]5-9+3x=-10+6+3x[/math] [math]3(n+1)=3n+1[/math] [math]v+2=v-2[/math] [math]n=n[/math] [math]\frac{1}{2}+x=\frac{1}{3}+x[/math]

Write the other side of this equation so that this equation is true for all values of [math]u[/math].[br][br][math]6(u-2)+2=[/math]

Write the other side of this equation so that this equation is true for no values of [math]u[/math]. [br][br][math]6(u-2)+2=[/math]

Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98.

[size=150]How many sets of two or more consecutive positive integers can be added to obtain a sum of 100?[/size]

Complete each equation so that it is true for all values of x.

[math]3x+6=3(x+\underscore\underscore)[/math]

[math]x-2=-(\underscore\underscore-x)[/math]

[math]\frac{15x-10}{5}=\underscore\underscore-2[/math]

Complete each equation so that it is true for no values of x.