Question 82·Easy·Linear Equations in One Variable
Solve for in the equation
(Express the answer as an integer)
For simple linear equations like this, your quickest method is to use inverse operations to isolate x: first get all x-terms on one side by adding or subtracting the smaller x-term from both sides, then move the constant terms to the opposite side, and finally perform any remaining basic operation (addition, subtraction, multiplication, or division) to solve for x. Always do the same operation to both sides and quickly check your solution by substituting it back into the original equation to avoid sign or arithmetic mistakes.
Hints
Get x terms together
Look at the terms with x on both sides: on the left and on the right. What operation can you use on both sides to combine them onto one side?
Then move the constants
After you have only one x-term (like ) on one side, move the constant number on that side to the other side by doing the opposite operation (adding instead of subtracting, or vice versa).
Solve and check
Once x is isolated, you should have an equation of the form . Plug that number back into the original equation to see if both sides are equal.
Desmos Guide
Graph both sides as functions
In Desmos, enter y = 3x - 7 on one line and y = 2x + 5 on another line. This will graph both sides of the equation as straight lines.
Find the intersection point
Look for the point where the two lines intersect. The x-coordinate of this intersection is the value of x that makes and equal. That x-value is the solution to the equation.
Step-by-step Explanation
Move all x-terms to one side
Start with the equation:
Subtract from both sides to get all the x-terms together:
This simplifies to:
Isolate x
Now get x by itself by adding 7 to both sides of the equation:
This simplifies to:
So the solution to the equation is . You can check by substituting this value back into the original equation to verify both sides are equal.