IM Alg2.3.7 Lesson: Inequivalent Equations

What do you notice? What do you wonder?
[list][*][math]x^2=4[/math][/*][*][math]x^2=\text{-}4[/math][/*][*][math](x-2)(x+2)=0[/math][/*][*][math]x=\sqrt{4}[/math][/*][/list]
Tyler was solving this equation:
[math]x^2-1=3[/math][br][br]He said, “I can add 1 to each side of the equation and it doesn’t change the equation. I get [math]x^2=4[/math]."[br][br]Priya said, “It does change the equation. It just doesn’t change the solutions!” Then she showed these two graphs.[br][br][img]data:image/png;base64,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[/img][br]How can you see the solution to the equation [math]x^2-1=3[/math] in Figure A?[br]
How can you see the solution to the equation [math]x^2=4[/math] in Figure B?[br]
Use the graphs to explain why the equations have the same solutions.[br]
Tyler said, “Now I can take the square root of each side to get the solution to [math]x^2=4[/math]. The square root of [math]x^2[/math] is [math]x[/math]. The square root of 4 is 2.” He wrote:[br][center][math]x^2=4[/math][br][math]\sqrt{x^2}=\sqrt{4}[/math][br][math]x=2[/math][/center]Priya said, “But the graphs show that there are [i]two[/i] solutions!” What went wrong?
Han was solving this equation:
[math]\frac{x+3}{2}=4[/math][size=150][br][br]He said, "I know that half of [math]x+3[/math] is 4. So [math]x+3[/math] must be 8, since half of 8 is 4. This means that [math]x[/math] is 5."[/size][br][br]Use Han's reasoning to solve this equation: [math](x+3)^2=4[/math]
What advice would you give to someone who was going to solve an equation like [math](x+3)^2=4[/math]?
Mai was solving this equation:
[math]\sqrt{x-1}=3[/math][br]She said, “I can square each side of the equation to get another equation with the same solutions.” Then she wrote:[br][center][math]\sqrt{x-1}=3[/math][br][math](\sqrt{x-1})^2=3^2[/math][br][math]x-1=9[/math][br][math]x=10[/math][/center]Check to see if her solution makes the original equation true.[br]
Andre said, “I tried your technique to solve [math]\sqrt{x-1}=\text{-}3[/math] but it didn’t work.” Why doesn’t it work?
Explain or show your reasoning.
Find the solution(s) to each of these equations, or explain why there is no solution.
[math]\sqrt{t+4}=3[/math]
[math]\text{-}10=\text{-}\sqrt{a}[/math]
[math]\sqrt{3-w}-4=0[/math]
[math]\sqrt{z}+9=0[/math]
Are there values of [math]a[/math] and [math]b[/math] so that the equation [math]\sqrt{t+a}=b[/math] has more than one solution? Explain your reasoning.
Cerrar

Información: IM Alg2.3.7 Lesson: Inequivalent Equations