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Math  /  Algebra

QuestionWhich equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number"? 6+2(x+4)=12(x−3)6+2(x+4)=12(3−x)(6+2)(x+4)=12(3−x)\begin{array}{l} 6+2(x+4)=\frac{1}{2}(x-3) \\ 6+2(x+4)=\frac{1}{2}(3-x) \\ (6+2)(x+4)=\frac{1}{2}(3-x) \end{array}

Studdy Solution

STEP 1

1. We need to translate a verbal statement into a mathematical equation.
2. The statement involves operations such as addition, multiplication, and division.
3. The statement includes a number, which we will represent with a variable, typically x x .

STEP 2

1. Identify and define the variable.
2. Translate the verbal statement into mathematical expressions.
3. Formulate the equation based on the expressions.
4. Compare the formulated equation with the given options.

STEP 3

Identify and define the variable. Let x x be the number referred to in the statement.

STEP 4

Translate the verbal statement into mathematical expressions.
- "twice the sum of a number and four": This means 2(x+4) 2(x + 4) . - "six added to": This means 6+ 6 + . - "one-half of the difference of three and the number": This means 12(3−x) \frac{1}{2}(3 - x) .

STEP 5

Formulate the equation based on the expressions.
The statement "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number" can be written as:
6+2(x+4)=12(3−x) 6 + 2(x + 4) = \frac{1}{2}(3 - x)

STEP 6

Compare the formulated equation with the given options.
The equation 6+2(x+4)=12(3−x) 6 + 2(x + 4) = \frac{1}{2}(3 - x) matches the second option provided:
6+2(x+4)=12(3−x) 6 + 2(x + 4) = \frac{1}{2}(3 - x)

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