Solve $-8x = 56$ for $x$.
Answer (2)
Divide both sides of the equation by -8: − 8 − 8 x = − 8 56
Simplify the equation: x = − 8 56
Calculate the value of x: x = − 7
The solution to the equation is: − 7
Explanation
Understanding the problem We are given the equation − 8 x = 56 and we need to solve for x . This means we want to isolate x on one side of the equation.
Isolating x To isolate x , we need to divide both sides of the equation by the coefficient of x , which is − 8 . So we have: − 8 x = 56 Divide both sides by − 8 :
− 8 − 8 x = − 8 56
Simplifying the equation Now, simplify the equation: x = − 8 56 x = − 7
Final Answer Therefore, the solution to the equation − 8 x = 56 is x = − 7 .
Examples
In real life, this type of problem can be used to determine how many hours someone needs to work to earn a certain amount of money. For example, if someone earns $8 per hour and needs to earn $56, we can use the equation − 8 x = − 56 (since the money is owed) to find that they need to work 7 hours.
To solve − 8 x = 56 , divide both sides by − 8 to isolate x , resulting in x = − 7 . The final solution is x = − 7 .
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