Question 85·Easy·Linear Equations in One Variable
For what value of does
?
For single-variable linear equations like this, first remove parentheses by distributing, then collect like terms by moving all terms to one side and constants to the other using inverse operations. Keep your work organized line by line, carefully track signs when adding or subtracting, and do a quick plug-in check with your solution to avoid small arithmetic errors.
Hints
Expand the left-hand side
First rewrite without parentheses by distributing the 3 to both and .
Group like terms
Once the parentheses are gone, get all the terms on one side of the equation and the constant numbers on the other side.
Isolate x
After you have one term on one side, use addition or subtraction to get by itself.
Desmos Guide
Graph both sides as separate functions
In Desmos, enter y = 3(x - 4) on one line and y = 2x + 5 on another line. These are the left and right sides of the equation written as functions.
Find the intersection point
Look for the point where the two graphs intersect and tap on it. The x-coordinate of this intersection is the value of that makes and equal.
Step-by-step Explanation
Distribute on the left side
Start with the equation:
Distribute the 3 on the left:
So the equation becomes:
Get all x-terms on one side
Subtract from both sides to collect the terms:
This simplifies to:
Isolate the variable
Add 12 to both sides to continue solving for :
Now the left side simplifies to , and the right side is a simple sum.
Compute, check, and state the answer
Compute the value of and verify by substitution:
Left side:
Right side:
Both sides are equal, so is correct. The correct answer choice is A) 17.