If , what is the value of ?
For linear equations in one variable that include parentheses, first distribute to remove parentheses, then combine like terms so all x-terms are on one side and all constants are on the other. Use inverse operations step by step (add/subtract, then multiply/divide) to isolate x, and if time allows, quickly plug your solution back into the original equation to verify both sides are equal.
Hints
Clear the parentheses first
Look at . What operation is implied between 3 and , and how can you rewrite this without parentheses?
Group like terms
Once you distribute, you will have an term and a constant term on each side. How can you get all the terms on one side of the equation?
Isolate x
After you have all the terms on one side and numbers on the other, what single operation will get by itself?
Desmos Guide
Enter the two sides as separate functions
In Desmos, type y = 3(x + 2) on one line and y = 5x - 6 on another line to graph both sides of the equation.
Find the intersection point
Look for the point where the two lines intersect. Tap or click on the intersection to see its coordinates; the x-coordinate of this point is the solution to the equation .
Alternative: Use a single expression
Alternatively, type 3(x + 2) - (5x - 6) and open a table for this expression. The value of that makes the expression equal to 0 is the solution to the equation.
Step-by-step Explanation
Distribute on the left side
Start with the equation:
Distribute the 3 to both and :
Move all x-terms to one side and constants to the other
Subtract from both sides to get the x-terms together:
Now add 6 to both sides to get the constants together:
Solve for x and check
You now have a simple equation with one step left:
Divide both sides by 2:
Quick check: substitute into the original equation.
- Left:
- Right:
Both sides are equal, so the solution is . This corresponds to choice C.