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Algebra / Linear equations in one variable Difficulty: Easy

$3$ more than $8$ times a number $x$ is equal to $83$ . Which equation represents this situation?

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Explanation

Choice D is correct. The given phrase “ $8$ times a number $x$ ” can be represented by the expression $8 x$ . The given phrase “ $3$ more than” indicates an increase of $3$ to a quantity. Therefore “ $3$ more than $8$ times a number $x$ ” can be represented by the expression $8 x plus 3$ . Since it’s given that $3$ more than $8$ times a number $x$ is equal to $83$ , it follows that $8 x plus 3$ is equal to $83$ , or $8 x + 3 = 83$ . Therefore, the equation that represents this situation is $8 x + 3 = 83$ .

Choice A is incorrect. This equation represents $3$ times the quantity $8$ times a number $x$ is equal to $83$ .

Choice B is incorrect. This equation represents $8$ times a number $x$ is equal to $3$ more than $83$ .

Choice C is incorrect. This equation represents $8$ more than $3$ times a number $x$ is equal to $83$ .