Question 25·Easy·Linear Equations in One Variable
If , what is the value of ?
(Express the answer as an integer)
For linear-equation questions that then ask for a related expression, first use inverse operations to isolate the variable: undo addition or subtraction, then undo multiplication or division. Once you have the variable’s value, substitute it carefully into the requested expression and follow the order of operations (multiply first, then add or subtract). Always double-check that you answered the question being asked (the new expression), not just the intermediate value of the variable.
Hints
Isolate y first
Before you can evaluate , you need to know the value of . Focus on solving the equation .
Undo operations step by step
In , think about which operation to undo first: the or the multiplication by 5. Use inverse operations (do the opposite) on both sides.
Use y to evaluate the new expression
Once you have found , substitute that number into and simplify carefully. Make sure you multiply before you add.
Desmos Guide
Find the value of y
In a Desmos expression line, type (22 + 3) / 5 to compute the value of from the equation . Note the numerical result Desmos shows.
Evaluate 4y + 1 using that y
In a new line, type 4 * (result) + 1, replacing result with the value of you just found (for example, 4 * 5 + 1 if ). The number Desmos outputs is the value of .
Step-by-step Explanation
Understand what is being asked
You are not being asked to find directly. Instead, you must:
- Solve the equation to find the value of .
- Use that value of to evaluate the new expression .
Solve the equation for y
Isolate in the equation .
Add 3 to both sides:
Now divide both sides by 5:
So the solution to the equation is .
Substitute y into 4y + 1
Now plug into the expression :
So, the value of is 21.