Variable equation:
2x + 5 = 17
Replacement set:
{x = 6}
Explanation:
To solve the equation 2x + 5 = 17, subtract 5 from both sides to isolate the term with the variable:
2x + 5 - 5 = 17 - 5
2x = 12
Then, divide both sides of the equation by 2 to solve for x:
2x / 2 = 12 / 2
x = 6
Thus, the solution is x = 6.
Now, let's find a classmate's problem to solve.
Classmate's problem:
4y - 6 = 3y + 8
Solution:
To solve the equation 4y - 6 = 3y + 8, we need to isolate the term with the variable.
First, we can subtract 3y from both sides:
4y - 3y - 6 = 3y - 3y + 8
y - 6 = 8
Next, to isolate y, we can add 6 to both sides:
y - 6 + 6 = 8 + 6
y = 14
Thus, the solution is y = 14.
Regarding the replacement set, it refers to a specific value or set of values that can be substituted for the variable in the equation to get an accurate solution. In the case of the equation 2x + 5 = 17, the replacement set {x = 6} is valid because when we substitute x = 6 into the equation, we get 2(6) + 5 = 12 + 5 = 17, which satisfies the equation.
When solving a classmate's problem or any other equation, it's important to check the validity of the replacement set by substituting the values back into the original equation to ensure they satisfy the equation.