Question 70·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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$|3z + 1| = 7$

What is one possible value of $z$ that satisfies the equation?

An absolute value equation with a positive number on one side can have two solutions: the expression inside the bars can be positive or negative. If the question asks for one possible value, you only need one solution. A Desmos regression can find it, but don't mistake the number outside the bars for the variable's value.

Hints

Hint 1
An absolute value is a distance from $0$ . Both $7$ and $-7$ are $7$ units from $0$ . What two values could the expression inside the bars have?
Hint 2
The question asks for one value, and every answer choice is positive. In a Desmos regression, replace $z$ with $x_1$ and restrict $x_1>0$ so Desmos finds a positive solution.

Step-by-step

Use the two-case idea, then Desmos
Step 1
Identify what can be inside the bars
An absolute value gives distance from $0$ . Since that distance is $7$ , the inside can be $7$ or $-7$ : $3z+1=7\quad\text{or}\quad 3z+1=-7$ . The inside expression, not $z$ by itself, equals one of those numbers.
Step 2
Find one positive solution
Every answer choice is positive, so ask Desmos for a positive solution. Replace $z$ with $x_1$ and type $\left|3x_1+1\right|\sim7\{x_1>0\}$ . The $\sim$ tells Desmos to find a value that makes the sides equal; the braces restrict that value to positive numbers. Under PARAMETERS, Desmos shows $x_1=2$ . So $z=2$ is one possible value. Choice A.

Question 70·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this