What are the solution(s) of $-\frac{1}{2} x+4=x+1$?
Answer (1)
Add 2 1 x to both sides: 4 = 2 3 x + 1 .
Subtract 1 from both sides: 3 = 2 3 x .
Multiply both sides by 3 2 : x = 2 .
The solution to the equation is 2 .
Explanation
Understanding the problem We are given the equation − 2 1 x + 4 = x + 1 and we need to find the value(s) of x that satisfy this equation.
Adding 2 1 x to both sides First, let's add 2 1 x to both sides of the equation to get rid of the fraction on the left side: − 2 1 x + 4 − 2 1 x + 4 + 2 1 x 4 = x + 1 = x + 1 + 2 1 x = 2 3 x + 1
Subtracting 1 from both sides Next, subtract 1 from both sides to isolate the term with x : 4 4 − 1 3 = 2 3 x + 1 = 2 3 x + 1 − 1 = 2 3 x
Multiplying by 3 2 Now, multiply both sides by 3 2 to isolate x : 3 3 ⋅ 3 2 2 = 2 3 x = 2 3 x ⋅ 3 2 = x
Final Answer Therefore, the solution to the equation is x = 2 .
Examples
Linear equations like this one are used in many real-world situations. For example, imagine you are comparing two cell phone plans. Plan A has a $4 monthly fee and charges $0.50 per gigabyte of data. Plan B has a $1 monthly fee and charges $1.00 per gigabyte of data. The equation we solved is similar to finding out how many gigabytes of data you would need to use for the two plans to cost the same amount. Understanding how to solve linear equations helps you make informed decisions in everyday life.
