Question 409·Easy·Math

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If $7 - 2k = 1$ , what is the value of $5k + 4$ ?

A linear equation has an unknown to the first power. Solve it by keeping both sides equal as you undo operations, or use a Desmos regression with $\sim$ in place of $=$ . The value of the unknown is not automatically the value the question asks for. Check whether you still need to evaluate another expression.

Hints

Hint 1
A regression can find the unknown that makes both sides equal. Replace $=$ with $\sim$ in the given equation. What value does Desmos show for $k$ under PARAMETERS?
Hint 2
Once you know $k$ , substitute its value into the entire expression $5k+4$ . The question asks for that expression's value, not for $k$ alone.

Step-by-step

Approach 1: Solve and evaluate in Desmos
Step 1
Find the value of $k$
Type $7-2k\sim1$ . The $\sim$ tells Desmos to use a regression to find the $k$ that makes both sides equal. Under PARAMETERS, Desmos shows $k=3$ .
Step 2
Evaluate what the question asks for
On the next line, type $5k+4$ . Desmos uses $k=3$ and prints $19$ . That's the value of $5k+4$ , rather than the value of $k$ . Choice B.

Approach 2: See why the solution is positive
Step 1
Leave the $k$ term by itself
Subtract $7$ from both sides of the equation so they stay equal:
$-2k=-6$
Step 2
Solve for $k$
Divide both sides by $-2$ :
$k=\frac{-6}{-2}$
A negative divided by a negative is positive:
$k=3$
Step 3
Find the requested value
Put $3$ in place of $k$ in the requested expression:
$5k+4=5(3)+4$
Multiply:
$5k+4=15+4$
Add:
$5k+4=19$
So $5k+4$ is $19$ . Choice B.

Question 409·Easy·Math

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