In the equation , what is the value of ?
For linear equations like this, first eliminate parentheses using the distributive property, then collect all variable terms on one side and constants on the other using the same operation on both sides. Once you have a simple equation like , isolate the variable by dividing, and as a quick check, plug your solution back into the original equation or compare both sides on Desmos to confirm they match.
Hints
Start with the distributive property
Look at the left side . How can you remove the parentheses by multiplying 4 by each term inside?
Collect like terms
Once you distribute, you will have an equation with terms on both sides. What operation can you use to move all the terms to one side of the equation?
Isolate the variable
After you have all the terms on one side, focus on getting by itself. What two inverse operations do you need to use to undo subtraction and multiplication?
Desmos Guide
Graph both sides of the equation
In Desmos, enter y = 4(2x - 3) on one line and y = 5x + 9 on another. These represent the left and right sides of the equation.
Find the intersection point
Use the cursor or tap on the graph where the two lines intersect. The x-coordinate of this intersection is the value of that makes true.
Step-by-step Explanation
Distribute the 4 on the left side
Apply the distributive property to :
So the original equation becomes
Move all k-terms to one side
Get the terms together by subtracting from both sides:
which simplifies to
Isolate k and solve
First undo the by adding 12 to both sides:
Now divide both sides by 3:
So the value of is , which corresponds to choice C.