We are given the linear equation 3 times open parenthesis x minus 2 close parenthesis equals 16. Our goal is to solve for the variable x. This equation has one variable and we need to isolate it to find its value.
To solve this equation, we first apply the distributive property. This means we multiply 3 by both terms inside the parentheses. So 3 times x gives us 3x, and 3 times negative 2 gives us negative 6. This transforms our equation to 3x minus 6 equals 16.
Now we want to isolate the term with x. To do this, we add 6 to both sides of the equation. On the left side, negative 6 plus 6 cancels out, leaving us with just 3x. On the right side, 16 plus 6 equals 22. So our equation becomes 3x equals 22.
To solve for x, we divide both sides of the equation by 3. On the left side, 3x divided by 3 gives us just x. On the right side, we have 22 divided by 3. This fraction can be expressed as a mixed number: 7 and 1 third, or as a decimal: approximately 7.333...
To verify our solution, we substitute x equals 22 thirds back into the original equation. First, we calculate what's inside the parentheses: 22 thirds minus 2. Converting 2 to thirds gives us 6 thirds. So we have 22 thirds minus 6 thirds, which equals 16 thirds. Now we multiply 3 by 16 thirds. The 3s cancel out, leaving us with 16. Since both sides of the equation equal 16, our solution is correct.
Let's summarize the steps to solve this linear equation. First, we started with the equation 3 times open parenthesis x minus 2 close parenthesis equals 16. Then we applied the distributive property to get 3x minus 6 equals 16. Next, we added 6 to both sides to isolate the variable term, resulting in 3x equals 22. Finally, we divided both sides by 3 to solve for x, giving us x equals 22 thirds or 7 and 1 third. We verified this solution by substituting it back into the original equation.