Question 67·Easy·Linear Equations in One Variable
What value of satisfies the equation ?
For one-variable linear equations like , quickly isolate the variable by reversing the operations in the opposite order they are applied: first undo any addition or subtraction, then undo multiplication or division. Always perform the same operation on both sides to keep the equation balanced, and simplify step by step to avoid sign or arithmetic mistakes before matching your solution to the answer choices.
Hints
Think about inverse operations
is being multiplied by 2 and then 5 is subtracted. Which operation will undo subtracting 5 from the left side?
Balance both sides
After you undo the subtraction, you will have an equation of the form . What operation will isolate from ?
Match your solution to the choices
Once you find the value of , check which answer choice shows that same number.
Desmos Guide
Enter the related functions
In Desmos, type y = 2x - 5 on one line and y = 27 on another line. These represent the two sides of the equation as functions of .
Find the intersection
Look for the point where the two graphs intersect and tap/click that point. The -coordinate of this intersection is the value of that satisfies the original equation.
Step-by-step Explanation
Identify the goal
The equation is . The goal is to isolate on one side of the equation by undoing the operations being applied to it.
Undo the subtraction
is being multiplied by 2 and then 5 is subtracted. Undo the subtraction first by adding 5 to both sides:
Undo the multiplication and find k
Now is being multiplied by 2. Undo this by dividing both sides by 2:
So the value of that satisfies the equation is , which corresponds to choice B.