Write a solvable variable equation and share it in the forum. Include a replacement set.
Find a problem one of your classmates has posted and solve it. Post your solution in the same discussion topic as the problem. If the problem is unsolvable, because of the way that it is written, explain why you cannot solve it. Comment on the validity of the replacement set.
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.