Solve the equation [tex]$12 x+6 y=24$[/tex] for [tex]$x$[/tex].
A. [tex]$x=24-6 y$[/tex]
B. [tex]$x=\frac{1}{2} y+2$[/tex]
C. [tex]$x=2-\frac{1}{2} y$[/tex]
D. [tex]$x=12(24-6 y)$[/tex]
Answer (2)
Subtract 6 y from both sides: 12 x = 24 − 6 y .
Divide both sides by 12: x = 12 24 − 6 y .
Simplify the expression: x = 12 24 − 12 6 y .
Obtain the final expression: x = 2 − 2 1 y . The answer is x = 2 − 2 1 y .
Explanation
Understanding the Problem We are given the equation 12 x + 6 y = 24 and we want to solve for x in terms of y . This means we want to isolate x on one side of the equation.
Isolating the x term First, we subtract 6 y from both sides of the equation to isolate the term with x : 12 x = 24 − 6 y
Solving for x Next, we divide both sides of the equation by 12 to solve for x : x = 12 24 − 6 y
Simplifying the expression Now, we simplify the expression for x by dividing each term in the numerator by 12: x = 12 24 − 12 6 y
Final simplification Finally, we simplify the fractions: x = 2 − 2 1 y
Examples
Solving for a variable is a fundamental skill in algebra and is used in many real-world applications. For example, imagine you are planning a party and have a budget of $24. You want to buy drinks that cost $6 per package and snacks that cost 12 p er i t e m . I f yo u l e t x b e t h e n u mb ero f s na c ki t e m s an d y$ be the number of drink packages, the equation 12 x + 6 y = 24 represents your budget constraint. Solving for x in terms of y allows you to determine how many snack items you can buy based on the number of drink packages you purchase. This helps you make informed decisions to stay within your budget.
To solve for x in the equation 12 x + 6 y = 24 , we isolate x by subtracting 6 y and dividing by 12. This gives the solution x = 2 − 2 1 y . The answer corresponds to option C.
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