Question 291·Medium·Algebra

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\tfrac23(x-3)-\tfrac16(x-3)=5

What value of $x$ satisfies the equation above?

Your answer

A linear equation has the unknown only to the first power. If the same parentheses appear in two terms, combine the numbers multiplying them without dropping the parentheses. Keep the repeated expression intact while you combine what multiplies it. On a timed test, a Desmos regression of the original equation can finish the solve without distributing.

Hints

Hint 1
The two terms are like terms because both contain the whole expression $x-3$ . Subtract the numbers multiplying that expression. What stays in parentheses after you combine them?
Hint 2
A regression can make Desmos find the unknown. Replace $x$ with $x_1$ and $=$ with $\sim$ in the original equation. Desmos reports the value of $x_1$ under PARAMETERS.

Step-by-step

Keep the parentheses together, then use Desmos
Step 1
Combine the matching terms
Both terms multiply $x-3$ , so they're like terms: they share the same expression. Combine their coefficients, the numbers multiplying $x-3$ :
$\frac23(x-3)-\frac16(x-3)=\left(\frac23-\frac16\right)(x-3).$
Keep the whole $x-3$ . You can't cancel it, because the $5$ on the right doesn't contain that factor.
Step 2
Find the new coefficient
Type $\frac23-\frac16$ in Desmos. It prints $0.5$ , or $\frac12$ . Replace the coefficient while keeping the parentheses:
$\frac12(x-3)=5.$
Step 3
Solve the original equation
Type the original equation as $\frac23(x_1-3)-\frac16(x_1-3)\sim5$ . Here $x_1$ is the unknown Desmos will find, and $\sim$ tells Desmos to find the value that makes both sides equal. The regression reports $x_1=13$ under PARAMETERS, so the value of $x$ that satisfies the equation is $13$ . Grid in 13.

Question 291·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this