Question

an equation is shown below. a student wants to remove the fractions to more easily solve the equation. which statement explains the best way to do this? a multiply the 2 terms with fractions by 2(3x - 1) because the reciprocal of 1/2 is 2 and the reciprocal of 1/(3x - 1) is (3x - 1)/1 and 2(3x - 1) is the product of the denominators in the terms with fractions. b multiply all 3 terms in the equation by 2(3x - 1) because 3x - 1 and 2 are the denominators in the terms with fractions. c multiply all 3 terms in the equation by 2(3x - 1) because the reciprocal of 1/2 is 2 and the reciprocal of 1/(3x - 1) is (3x - 1)/1 and 2(3x - 1) is the product of the denominators in the terms with fractions. d multiply the 2 terms with fractions by 2(3x - 1) because 3x - 1 and 2 are the denominators in the terms with fractions.

Explanation:

Step1: Identify the denominators

The denominators in the fractions of the given equation are \(2\) and \(3x - 1\).

Step2: Determine the way to clear fractions

To clear the fractions in an equation, we multiply each term of the equation by the least - common multiple (LCM) of the denominators. Here, the LCM of \(2\) and \(3x - 1\) is \(2(3x - 1)\). We need to multiply all terms in the equation by \(2(3x - 1)\) to remove the fractions.

Answer:

C. Multiply all 3 terms in the equation by \(2(3x - 1)\) because \(2\) and \(3x - 1\) are the denominators in the terms with fractions.