Ask AI: 1/3(6q–2)=4q–7/3q–1/2

First, we need to solve the equation step by step. Here's the given equation: 1/3(6q–2)=4q–7/3q–1/2 Let's start by distributing 1/3 to both terms inside the parentheses: (1/3 * 6q) - (1/3 * 2) = 4q - 7 / 3q - 1/2 2q - 2/3 = 4q - 7 / 3q - 1/2 Now, we need to get rid of the fractions. To do this, find the least common denominator (LCD). The LCD of 3 and 2 is 6. Multiply each term by 6: 6(2q - 2/3) = 6(4q - 7 / 3q - 1/2) This simplifies to: 12q - 4 = (6 * 4q - 7) / 3q - (6 * 1) / 2 12q - 4 = (24q - 42) / 3q - 3 Now, get rid of the parentheses: 12q - 4 = 24q - 42 - 3q Combine like terms: 12q - 4 = 21q - 42 To isolate the variable (q) on one side, we need to shift terms around: 12q - 21q = 42 - 4 -9q = 38 Now, divide by -9 to find the value of q: q = 38 / -9 q ≈ -4.22 (rounded to 2 decimal places) So, the approximate value of q is -4.22.