Question 166·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Which of the following values of $x$ satisfies the equation

x^3 = -27

A lone $x^3$ is the cue to find a cube root: the number that gives the right side when cubed. On a timed test, enter the equation as a Desmos regression to find that number. An odd power keeps a negative input negative. Don’t divide the right side by $3$ ; the exponent means repeated multiplication, not multiplication by $3$ .

Hints

Hint 1
A cube means multiplying a number by itself three times. Three negative factors give a negative result, so what sign must $x$ have when its cube is negative?
Hint 2
For an equation with one unknown, use a Desmos regression to match the two sides. Replace $x$ with $x_1$ and $=$ with $\sim$ ; Desmos will report the value it finds under PARAMETERS.

Step-by-step

Use the sign, then solve in Desmos
Step 1
Determine the sign of $x$
A cube multiplies a number by itself three times: $x^3=x\cdot x\cdot x$ . The result is negative, so $x$ must be negative. Three negative factors produce a negative result; three positive factors don’t.
Step 2
Find the value that cubes to $-27$
Type $x_1^3\sim-27$ in Desmos. The subscript in $x_1$ makes it a value to find rather than an $x$ to graph, and $\sim$ asks Desmos to match the sides. Under PARAMETERS, Desmos shows $x_1=-3$ . Check the cube: $(-3)^3=-27$ , so $x=-3$ satisfies the equation. Choice B.

Question 166·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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