How many Solutions?

Choose the correct solution to the question in the applet below. Then click on “Next” to continue. Your score is recorded at the top right.

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Sort Equations into Categories.

Here are some cards. Solve each equation. Then, sort the cards into categories.

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Find Number of Solutions of an Equation.

(A). Consider the unfinished equation What is the number of solutions the equation would have with the following expression on the right hand side?

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(B). For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions).

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(C). For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions).

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(D). For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions).

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(E). For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions).

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(F). For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions).

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(G). Decide whether each equation is true for all, one, or no values of x.

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Sort out Equations.

(A). Select all the equations that are true for all values.

(B). Select all the equations that are true for no values.

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The points (-2, 0) and (0, -6) are each on the graph of a linear equation. 

Explain your reasoning.

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Solve each of the equations below.

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Lin was looking at the equation 2– 32 + 4(3 – 2462) = 14. She said, “I can tell right away there are no solutions, because on the left side, you will have 2 + 12 and a bunch of constants, but you have just on the right side.” Do you agree with Lin? Explain your reasoning.