Solve the equation for the given variable:
[tex]$-20 x+8=-2 x+15$[/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 (2)
Add 20 x to both sides: 8 = 18 x + 15 .
Subtract 15 from both sides: − 7 = 18 x .
Divide both sides by 18: x = − 18 7 .
The solution is x = − 18 7 .
Explanation
Understanding the Problem We are given the equation − 20 x + 8 = − 2 x + 15 and our goal is to solve for the variable x . We will isolate x by performing algebraic operations on both sides of the equation.
Adding 20x to Both Sides First, we want to get all the x terms on one side of the equation. Let's add 20 x to both sides of the equation: − 20 x + 8 + 20 x = − 2 x + 15 + 20 x 8 = 18 x + 15
Subtracting 15 from Both Sides Next, we want to isolate the x term. To do this, we subtract 15 from both sides of the equation: 8 − 15 = 18 x + 15 − 15 − 7 = 18 x
Dividing by 18 Finally, to solve for x , we divide both sides of the equation by 18: 18 − 7 = 18 18 x x = − 18 7
Final Answer The fraction − 18 7 is already in its simplest form, as 7 and 18 have no common factors other than 1. Therefore, the solution to the equation is x = − 18 7 .
Examples
Solving linear equations is a fundamental skill in algebra and is used in various real-life situations. For example, imagine you are buying a new phone. The phone costs $200, and you have a coupon for 15% off. You can set up a linear equation to find the final price of the phone after applying the discount. Similarly, linear equations are used in physics to calculate motion, in finance to calculate interest, and in many other fields.
To solve the equation − 20 x + 8 = − 2 x + 15 , we isolate the variable x through a series of algebraic steps, culminating in the solution x = − 18 7 . This fraction is simplified, as 7 and 18 share no common factors. Thus, the solution reflects the value of x .
;
