Question 329·Medium·Math

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If $7-2(3x-4)=5x+1$ , what is $x$ ?

A linear equation has the unknown only to the first power. If $x$ appears on both sides, a Desmos regression can solve the original equation without rearranging it. First watch the negative factor outside the parentheses: it multiplies both terms inside. Changing a sign there means you’re solving a different equation.

Hints

Hint 1
The distributive property says the number outside parentheses multiplies each term inside. Multiply $-2$ by $3x$ and by $-4$ separately. What sign does the second product have?
Hint 2
A solution makes both sides of an equation equal. To find it in Desmos, replace every $x$ with $x_{1}$ and $=$ with $\sim$ . Use the original equation so an error in distributing can’t change what you solve.

Step-by-step

Check the sign, then solve in Desmos
Step 1
Distribute the negative factor
The distributive property multiplies $-2$ by both terms inside $3x-4$$:7-2(3x-4)=5x+1\quad\Longrightarrow\quad 7-6x+8=5x+1$ .Negative $2$ times negative $4$ gives positive $8$ . Writing $-8$ would change the equation.
Step 2
Read the exact value of x
Type the original equation as $7-2(3x_{1}-4)\sim5x_{1}+1$ . Desmos uses $x_{1}$ as the number to find, and $\sim$ tells it to make the two sides equal. Under PARAMETERS, it shows $x_{1}\approx1.272727\ldots$ . Type $x_{1}$ on the next line and tap its fraction button to see $\frac{14}{11}$ . So $x=\frac{14}{11}$ . Choice C.

Question 329·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this