Solve the equation [tex]$6 x-3=-12$[/tex].
Answer (2)
Add 3 to both sides of the equation: 6 x − 3 + 3 = − 12 + 3 , which simplifies to 6 x = − 9 .
Divide both sides by 6: 6 6 x = 6 − 9 .
Simplify the fraction: x = − 6 9 .
Reduce the fraction to its simplest form: x = − 2 3 .
The solution to the equation is − 2 3 .
Explanation
Understanding the Problem We are given the equation 6 x − 3 = − 12 . Our goal is to isolate x on one side of the equation to find its value.
Adding 3 to Both Sides First, we add 3 to both sides of the equation to eliminate the -3 on the left side: 6 x − 3 + 3 = − 12 + 3
Simplifying the Equation This simplifies to: 6 x = − 9
Dividing by 6 Next, we divide both sides of the equation by 6 to isolate x :
6 6 x = 6 − 9
Simplifying the Fraction Simplifying the fraction, we get: x = − 6 9 x = − 2 3
Final Answer Therefore, the solution to the equation is x = − 2 3 .
Examples
Imagine you're buying concert tickets online. The base price is $6 per ticket, but there's a discount of $3 applied to your total. If your final cost is $12, this problem helps you determine how many tickets you bought. By solving the equation 6 x − 3 = − 12 , you find that x = -3/2, which doesn't make sense in this context because you can't buy a negative or fractional number of tickets. This highlights that while the math is correct, the real-world application needs to make sense!
To solve the equation 6 x − 3 = − 12 , we add 3 to both sides, resulting in 6 x = − 9 . Dividing both sides by 6 gives x = − 6 9 , which simplifies to x = − 2 3 . Therefore, the solution is x = − 2 3 .
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