Question 365·Medium·Math

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5(4 - x) + 3x = 2(x + 7) + 1

If $x$ satisfies the equation above, what is the value of $2x - 5$ ?

An equation with $x$ on both sides and no powers above $1$ is a linear equation. Desmos can find $x$ with a regression, which uses $\sim$ to solve an equality instead of drawing a graph. Find $x$ , then evaluate the expression the question actually asks for. Stopping at $x$ or $2x$ leaves the job unfinished.

Hints

Hint 1
A solution is a value of $x$ that makes both sides equal. To find it in Desmos without distributing, change every $x$ to $x_1$ and replace the equal sign with $\sim$ .
Hint 2
The solution may not be the answer. After Desmos finds $x_1$ , type the whole requested expression $2x_1-5$ on a new line. What happens after you double $x_1$ ?

Step-by-step

Solve and evaluate in Desmos
Step 1
Find the value of x
Type $5(4-x_1)+3x_1\sim2(x_1+7)+1$ . Change every $x$ to $x_1$ and $=$ to $\sim$ so Desmos solves for $x_1$ instead of graphing the equation. Under PARAMETERS, it reports $x_1=1.25$ , so $x=1.25=\frac54$ .
Step 2
Evaluate what the question asks for
On the next line, type $2x_1-5$ . Desmos prints $-2.5$ ; its fraction button shows $-\frac52$ . The $-5$ comes after doubling $x$ , so stopping at $2x=\frac52$ gives the wrong value. The value of $2x-5$ is $-\frac52$ . Choice D.

Question 365·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this