Question 55·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

0 / 233

Given the equation

|2x - 7| = 3,

which value is a solution to the equation?

An absolute value is a distance from zero. If it equals a positive number, the expression inside the bars can be either positive or negative. Desmos can find a solution to the equation with a regression; restrict it to one sign when there are two possible solutions. Keep both signs of the inside in mind.

Hints

Hint 1
Absolute value removes a minus sign: both $3$ and $-3$ have an absolute value of $3$ . What two values could the expression inside the bars equal?
Hint 2
A Desmos regression finds a value of $x_1$ that makes an equation work. To find the negative-inside case, restrict the search to values where $2x_1-7<0$ .

Step-by-step

Find one solution with a restricted regression
Step 1
Account for both signs inside the bars
Absolute value is distance from zero. The given distance is $3$ , so the expression inside the bars has two possibilities:
$2x-7=3\quad\text{or}\quad 2x-7=-3.$
Solving only the positive-inside case could miss a solution.
Step 2
Find a solution from the negative-inside case
Type $|2x_1-7|\sim3\{2x_1-7<0\}$ in Desmos. Change $x$ to $x_1$ and $=$ to $\sim$ so Desmos solves for a value instead of graphing the equation. The condition keeps the inside negative, selecting that case. Under PARAMETERS, Desmos shows $x_1=2$ . So $x=2$ is a solution to the original equation. Choice B.

Question 55·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