Solve the equation for the given variable:
[tex]2 x-2=19[/tex]
If your answer is a fraction, write it in fraction form and reduce it completely. Do NOT convert to decimals.
Answer: [tex]x=[/tex] $\square$
Answer (1)
Add 2 to both sides of the equation: 2 x − 2 + 2 = 19 + 2 .
Simplify the equation: 2 x = 21 .
Divide both sides by 2: 2 2 x = 2 21 .
The solution is: x = 2 21 .
Explanation
Understanding the Problem We are given the equation 2 x − 2 = 19 and our goal is to solve for the variable x . This means we want to isolate x on one side of the equation.
Adding 2 to Both Sides First, we add 2 to both sides of the equation to eliminate the -2 on the left side: 2 x − 2 + 2 = 19 + 2
Simplifying the Equation This simplifies to: 2 x = 21
Dividing by 2 Next, we divide both sides of the equation by 2 to isolate x :
2 2 x = 2 21
Final Answer This simplifies to: x = 2 21 Since 21 and 2 have no common factors other than 1, the fraction is already in its simplest form.
Examples
Imagine you're buying tickets to a concert. Each ticket costs $2, and there's a service fee of $2. If your total bill is $19, this equation helps you figure out how many tickets you bought. By solving for x, you determine the number of tickets purchased before the service fee was added. This kind of problem-solving is useful in budgeting, shopping, and many other real-life scenarios where you need to calculate quantities based on fixed costs and totals.
