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3(3/4x+2 1/2)=5x

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1 Answer

Tori, find you have to focus on the mixed number in the equation, that is, 2½. It is preferable to convert this mixed number into a fraction. First, multiply the denominator 2 by the whole number 2. Then add 1 to the product.

2½ = (2 * 2 + 1)/2 = 5/2

Now, the equation is written as 3[(3/4)x + (5/2)] = 5x.

The next step is the use of the distributive property on the left side of the equation. You have to multiply 3 to each term between the brackets.

3[(3/4)x] + 3(5/2) = 5x

(9/4)x + (15/2) = 5x

Since there are fractions seen on the preceding step, it is convenient to get rid of these rational numbers multiplying each term in the equation by the least common denominator (LCD) of the terms. Focusing on each denominator, where the term 5x can be re-written as (5x/1), the LCD of the denominators is 4. (This value is found by finding the least common multiple of each denominator.) The LCD is then multiplied by each term.

4[(9/4)x + 4(15/2)] = (5x)(4)

4[(9/4)x] + 4(15/2) = 20x

(36/4)x + (60/2) = 20x

9x + 30 = 20x

Now comes the part where the like terms are used. For the next step, subtract 9x on both sides.

9x + 30 - 9x = 20x - 9x

30 = 11x

Now divide each side by 11.

30 / 11 = 11x / 11

30/11 = x