What is the solution to this equation?
[tex]5(x-4)=3 x+4[/tex]
A. [tex]x=-8[/tex]
B. [tex]x=3[/tex]
C. [tex]x=-2[/tex]
D. [tex]x=12[/tex]
Answer (1)
Expand the left side of the equation: 5 ( x − 4 ) = 5 x − 20 .
Rewrite the equation as 5 x − 20 = 3 x + 4 .
Isolate x by subtracting 3 x from both sides and adding 20 to both sides: 2 x = 24 .
Divide both sides by 2 to find the solution: x = 12 .
Explanation
Problem Analysis We are given the equation 5 ( x − 4 ) = 3 x + 4 and asked to find the solution from the options A. x = − 8 , B. x = 3 , C. x = − 2 , D. x = 12 . Our goal is to isolate x on one side of the equation to determine its value.
Expanding the Equation First, we expand the left side of the equation by distributing the 5: 5 ( x − 4 ) = 5 x − 20
Rewriting the Equation Now we rewrite the equation: 5 x − 20 = 3 x + 4
Isolating x Terms Next, we want to get all the x terms on one side of the equation. We can subtract 3 x from both sides: 5 x − 3 x − 20 = 3 x − 3 x + 4 2 x − 20 = 4
Isolating the x Term Now, we want to isolate the x term. We can add 20 to both sides of the equation: 2 x − 20 + 20 = 4 + 20 2 x = 24
Solving for x Finally, we divide both sides by 2 to solve for x :
2 2 x = 2 24 x = 12
Final Answer Comparing our solution x = 12 with the given options, we see that the correct answer is D. x = 12 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and proportions. For example, if you are buying items at a store and want to calculate the total cost, or if you are planning a road trip and want to determine how long it will take to reach your destination, you can use linear equations to model and solve these problems. Understanding how to solve linear equations is a fundamental skill that enables you to make informed decisions and solve practical problems in various real-world scenarios.
