Question 73·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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If $(2t - 1)^2 = 9$ , which of the following is a possible value of $t$ ?

A squared expression can equal a positive number in two ways: the expression can be positive or negative. If the question asks for one possible value, you don't need to find both. A Desmos regression can solve the equation directly; when every choice is positive, restrict it to positive values. Don't confuse the number being squared with the result of squaring it.

Hints

Hint 1
A square root of $9$ is a number whose square is $9$ . Both $3$ and $-3$ work, so what two values could the expression inside the parentheses have?
Hint 2
A Desmos regression finds a value that makes two sides match, but it may find only one solution. Since every choice is positive, what restriction would make it look for a positive value?

Step-by-step

Use the square, then a Desmos regression
Step 1
Identify the two values that could be squared
Because $3^2=9$ and $(-3)^2=9$ , the squared expression $2t-1$ could equal either number:
$2t-1=3\quad\text{or}\quad 2t-1=-3.$
Both $3$ and $-3$ square to $9$ . Don't set $2t-1=9$ : $9$ is the result of squaring, not the number being squared.
Step 2
Find a positive possible value
Every answer choice is positive, so restrict Desmos to positive values. Type $(2x_1-1)^2\sim9\{x_1>0\}$ . Replace $t$ with $x_1$ because Desmos solves for a subscripted variable in a regression; $\sim$ tells it to match the two sides. Under PARAMETERS, Desmos shows $x_1=2$ . So $t=2$ is a possible value. Choice C.

Question 73·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

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Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

Lessons that teach this