Classify the following equation and show your work for 7x + 4 = 18 and tell if it is a) true b) false c) open
Choose the correct answer
The equation 7x + 4 = 18 is a simple linear equation in one variable x.
To determine if the equation is true, false, or open, we need to solve it for x and see if it satisfies the equation.
7x + 4 = 18
Subtracting 4 from both sides:
7x = 14
Dividing both sides by 7:
x = 2
Now we substitute the value of x back into the original equation:
7(2) + 4 = 14 + 4 = 18
Since the equation holds true when x = 2, the answer is a) true.
I understand dividing both side by 7 we get x = 2. Since the value of x can be determined the equation is an OPEN equation, meaning it has a solution
I apologize for the confusion in my previous response. You are correct. Since the value of x can be determined and the equation has a solution, the correct answer is c) open. Thank you for pointing that out.
To determine the classification of the equation 7x + 4 = 18, we need to solve it step by step.
Step 1: Begin by subtracting 4 from both sides of the equation:
7x + 4 - 4 = 18 - 4
This simplifies to:
7x = 14
Step 2: Divide both sides of the equation by 7 to isolate the variable x:
(7x)/7 = 14/7
This simplifies to:
x = 2
Now that we have solved the equation, we can determine its classification:
The equation is true if the value we obtained for x satisfies the original equation. Substituting x = 2 into the original equation:
7(2) + 4 = 18
14 + 4 = 18
18 = 18
Since both sides of the equation are equal, the equation is true.
Therefore, the correct answer is a) true