Question 586·Easy·Algebra

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If $3(x + 2) = 5x - 6$ , what is the value of $x$ ?

A linear equation can have the unknown on both sides. For a timed solve, enter the distributed equation as a Desmos regression: change $x$ to $x_1$ and $=$ to $\sim$ , then read the value Desmos finds. If you solve by hand, multiply every term inside parentheses and don’t stop while a coefficient is still attached to $x$ .

Hints

Hint 1
The distributive property says a number outside parentheses multiplies every term inside. What do you get when the $3$ multiplies the $x$ and then the $2$ ?
Hint 2
A Desmos regression finds a number that makes both sides equal. Use $x_1$ as the number to find, replace $=$ with $\sim$ , and read the result under PARAMETERS.

Step-by-step

Approach 1: Distribute, then solve in Desmos
Step 1
Distribute the 3
Apply the distributive property: the $3$ multiplies both terms in $(x+2)$ . A number outside parentheses multiplies every term inside. So the equation becomes:
$3x+6=5x-6.$
Step 2
Find the value of x
Type the distributed equation as $3x_1+6\sim5x_1-6$ . The $\sim$ tells Desmos to fit $x_1$ rather than graph an equation in $x$ . Under PARAMETERS, it shows $x_1=6$ . Since $x_1$ stands for the question’s $x$ , the value of $x$ is $6$ . Choice C.

Approach 2: Keep both sides equal by hand
Step 1
Put the x-terms on one side
Start with $3x+6=5x-6$ , the distributed equation above. Subtract $3x$ from both sides so the $x$ -terms are together:
$6=2x-6.$
Step 2
Isolate the x-term
Add $6$ to both sides to remove the $-6$ beside $2x$ :
$12=2x.$
Step 3
Solve for x
$12$ is the value of $2x$ , not yet $x$ . Divide both sides by $2$ :
$x=6.$
So the value of $x$ is $6$ . Choice C.

Question 586·Easy·Algebra

Strategy

Hints

Step-by-step

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