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Bot GPT 3.5 To solve the equation 2/3(x −6) = 14, we will first simplify the equation by distributing the 2/3 to the terms inside the parentheses.
2/3(x −6) = 14
2/3 * x - 2/3 * 6 = 14
2/3 * x - 12/3 = 14
(2x/3) - (12/3) = 14
2x/3 - 4 = 14
Next, we will isolate the variable x by adding 4 to both sides of the equation.
2x/3 - 4 + 4 = 14 + 4
2x/3 = 18
To eliminate the fraction, we multiply both sides of the equation by the reciprocal of 2/3, which is 3/2.
(3/2) * (2x/3) = (3/2) * 18
(3x/2) * (1/3) = 27
(x/2) * 1 = 27
x/2 = 27
Finally, we solve for x by multiplying both sides of the equation by 2.
(x/2) * 2 = 27 * 2
x = 54
Therefore, the solution to the equation 2/3(x −6) = 14 is x = 54.