Question

What is the solution of |3x-2|=7

Answer 1

x = 3

or

x = -5/3

Explanation:

We can define the equation:

`|3x - 2| = 7`

without the absolute value by splitting it into two equations:

`3x - 2 = 7` OR
`-(3x - 2) = 7`

Then, we can solve for x in each equation.

`\begin{aligned}3x - 2 = 7\\3x = 9\\ \boxed{x = 3}\end{aligned}` OR
`\begin{aligned}-(3x - 2) = 7\\-3x + 2 = 7\\3x = -5\end{aligned} \\ \\\text{ }\ \ \ \ \ \: \ \ \ \ \, \boxed{ x = -(5)/(3)}`

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Note that the expression inside the vertical bars can be positive or negative because the absolute value operator makes anything within it positive. This is why it can be split into two equations — one where the expression inside the absolute value is positive and one where it is negative.