Question 52·Easy·Linear Equations in One Variable
If , what value of satisfies the equation?
For one-variable linear equations of the form , solve quickly by isolating the variable with inverse operations: subtract or add to remove the constant term on the variable’s side, then divide by the coefficient of the variable. Keep the equation balanced by doing the same operation to both sides, and if you have a moment, substitute your solution back into the original equation to confirm it makes both sides equal.
Hints
Isolate the term with
Look at . What operation will remove the from the left side? Do the same operation to both sides of the equation.
Finish isolating
Once you have an equation of the form , what operation will turn into just ? Apply that operation to both sides.
Check your solution
After you find a value for , plug it back into and see if you really get 23.
Desmos Guide
Graph both sides of the equation
In Desmos, use as the variable. Enter the two expressions as separate functions:
- Type
y = 5x + 3 - Type
y = 23
Find the intersection
Look for the point where the line and the horizontal line intersect. Tap that point; the x-coordinate of the intersection is the value that satisfies the original equation .
Step-by-step Explanation
Undo the addition
The equation is . To start isolating , remove the by subtracting 3 from both sides:
This simplifies to:
Solve for the variable
Now . To get alone, divide both sides by 5 (the coefficient of ):
So . The value of that satisfies the equation is 4, which corresponds to choice C.