Question 516·Medium·Algebra

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Given the equation

$8x - 5 = 3(2x + 1) + x$

what is the value of $x$ ?

An equation with one unknown on both sides is a linear equation when the unknown has no power above $1$ . Check which terms are inside the parentheses, then use a Desmos regression to find the value that makes both sides equal. Multiplying a term outside the parentheses changes the equation and can lead to a tempting wrong answer.

Hints

Hint 1
Use the distributive property: the $3$ multiplies each term inside $(2x+1)$ . The final $+x$ is outside those parentheses. What does the right side look like after you distribute?
Hint 2
For an equation with one unknown, a Desmos regression can find the value that makes both sides equal. Replace every $x$ with $x_{1}$ and the equals sign with $\sim$ ; keep the parentheses unchanged.

Step-by-step

Check the parentheses, then solve in Desmos
Step 1
Distribute only inside the parentheses
Use the distributive property: multiply $3$ by both $2x$ and $1$ . The final $+x$ is outside the parentheses, so it stays as $+x$ . Rewrite the equation:
$8x-5=6x+3+x.$
Only terms inside the parentheses get multiplied by $3$ .
Step 2
Find the value that makes both sides equal
Type the original equation in Desmos as $8x_{1}-5\sim3(2x_{1}+1)+x_{1}$ . Replace every $x$ with $x_{1}$ so Desmos solves for a number, and replace $=$ with $\sim$ to run a regression. Under PARAMETERS, Desmos shows $x_{1}=8$ . So the value of $x$ is $8$ . Choice C.

Question 516·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this