Question 997·Medium·Math

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Which of the following values of $x$ satisfies the equation $(x+5)(x-1)+3=(x+2)(x+4)$ ?

Products on both sides can disguise a linear equation. Check the $x^2$ terms first: if they match, they cancel, leaving only $x$ and number terms. On a timed test, enter the original equation as a Desmos regression instead of expanding every product. Keep the constants in each product intact; multiplying them incorrectly changes the solution.

Hints

Hint 1
Multiplying the $x$ terms in each product gives $x^2$ . Those matching terms cancel when you subtract $x^2$ from both sides. What kind of terms are left?
Hint 2
A regression can find the input that makes two sides equal. Change every $x$ to $x_1$ and the equals sign to $\sim$ ; Desmos will report the value of $x_1$ under PARAMETERS.

Step-by-step

Spot the cancellation, then use Desmos
Step 1
Recognize the hidden linear equation
Each product contains $x\cdot x=x^2$ . So the $x^2$ terms match on the two sides and cancel when you subtract $x^2$ from both. Only $x$ and number terms remain. That's a linear equation: the highest remaining power of $x$ is $1$ .
Step 2
Find the value that makes both sides equal
Type $(x_1+5)(x_1-1)+3\sim(x_1+2)(x_1+4)$ in Desmos. Ordinary $x$ is graphed; $x_1$ with $\sim$ tells Desmos to solve for the input. Under PARAMETERS, it shows $x_1=-5$ . So the value of $x$ that satisfies the equation is $-5$ . Choice D.

Question 997·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this