Linear Equation Ten added to the product of a number and three is equal to twice the number. Write this statement as an equation.
10(x+3) = 2x
3x +10 = 2x
3(x+10) = 2x
10x + 3 = 2x
视频信息
答案文本
视频字幕
Let's translate this word problem step by step. First, we identify the unknown number as x. The product of a number and three becomes 3x. Ten added to this gives us 10 plus 3x. Twice the number is 2x. Setting them equal gives us the equation 10 plus 3x equals 2x, which can be written as 3x plus 10 equals 2x.
Now let's analyze each multiple choice option. Option A shows 10 times the quantity x plus 3, which doesn't match our translation. Option C shows 3 times the quantity x plus 10, also incorrect. Option D has 10x plus 3, which reverses the terms. Option B shows 3x plus 10 equals 2x, which correctly represents our word problem. The answer is B.
Let's solve our equation 3x plus 10 equals 2x. First, subtract 2x from both sides to get x plus 10 equals 0. Then subtract 10 from both sides to get x equals negative 10. Let's verify our answer by substituting back: 3 times negative 10 plus 10 equals negative 30 plus 10, which equals negative 20. And 2 times negative 10 also equals negative 20. Our solution is correct.
When translating word problems to equations, follow these key strategies. The product of a number and 3 becomes 3x. Ten added to something means 10 plus that expression. Twice a number is 2x. Is equal to becomes the equals sign. Avoid common mistakes like misplacing parentheses, confusing the order of terms, or incorrect grouping. The correct translation is 3x plus 10 equals 2x.
To summarize, we successfully translated the word problem into a linear equation. The unknown number is x, the product of the number and three is 3x, ten added to this gives us 3x plus 10, and twice the number is 2x. Setting them equal gives us 3x plus 10 equals 2x. The correct answer is option B. When solved, this equation gives us x equals negative 10.