Solve the following equation for $x$.
$3 x-9=-33$
Answer (2)
Add 9 to both sides of the equation: 3 x − 9 + 9 = − 33 + 9 , which simplifies to 3 x = − 24 .
Divide both sides by 3: 3 3 x = 3 − 24 .
Simplify to find the value of x : x = − 8 .
The solution to the equation is − 8 .
Explanation
Understanding the problem We are given the equation 3 x − 9 = − 33 and we need to solve for x .
Adding 9 to both sides To isolate x , we first add 9 to both sides of the equation: 3 x − 9 + 9 = − 33 + 9
Simplifying the equation Simplifying both sides, we get: 3 x = − 24
Dividing by 3 Now, we divide both sides by 3 to solve for x :
3 3 x = 3 − 24
Finding the value of x Simplifying, we find the value of x :
x = − 8
Final Answer Therefore, the solution to the equation 3 x − 9 = − 33 is x = − 8 .
Examples
In real life, this type of equation can be used to calculate how many items you need to sell to reach a certain profit goal. For example, if you sell items for $3 each, have a fixed cost of $9, and want to make a profit of $33, you can use the equation 3 x − 9 = 33 to find out how many items you need to sell. By solving for x , you determine the number of items needed to reach your profit goal. Understanding how to solve linear equations is a fundamental skill that can be applied to various financial and business scenarios.
By adding 9 to both sides of the equation 3 x − 9 = − 33 to isolate the variable, we simplify it to 3 x = − 24 . Dividing both sides by 3 leads us to the solution x = − 8 . Therefore, the final answer is x = − 8 .
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