What is the solution to this equation?
$-4 x+2=26$
A. $x=-6$
B. $x=6$
C. $x=-7$
D. $x=7$
Answer (1)
Subtract 2 from both sides of the equation: − 4 x = 24 .
Divide both sides by -4: x = − 4 24 .
Simplify the equation.
The solution to the equation is: x = − 6
Explanation
Understanding the Problem We are given the equation − 4 x + 2 = 26 and we need to find the value of x that satisfies this equation.
Isolating the x term To solve for x , we first need to isolate the term with x on one side of the equation. We can do this by subtracting 2 from both sides of the equation: − 4 x + 2 − 2 = 26 − 2
Simplifying the equation Simplifying both sides, we get: − 4 x = 24
Solving for x Now, to solve for x , we need to divide both sides of the equation by -4: − 4 − 4 x = − 4 24
The solution Simplifying, we find: x = − 6
Final Answer Therefore, the solution to the equation − 4 x + 2 = 26 is x = − 6 .
Examples
Linear equations like this are used in everyday situations, such as calculating the cost of items with a discount or determining how many hours you need to work to earn a certain amount of money. For example, if a store offers a $2 discount and you want to buy an item that costs $26, you can use the equation − 4 x + 2 = 26 to determine the original price of the item before the discount if the discount was 4 times some value x.
