Solve the equation.
$5 x+8-3 x=-10$
Answer (1)
Combine like terms: 5 x − 3 x + 8 = − 10 becomes 2 x + 8 = − 10 .
Subtract 8 from both sides: 2 x = − 18 .
Divide by 2: x = − 9 .
The solution to the equation is − 9 .
Explanation
Problem Analysis We are given the equation 5 x + 8 − 3 x = − 10 and asked to solve for x . Our goal is to isolate x on one side of the equation.
Combining Like Terms First, we combine like terms on the left side of the equation. We have 5 x and − 3 x , which combine to give 2 x . So the equation becomes 2 x + 8 = − 10 .
Isolating the x Term Next, we want to isolate the term with x . To do this, we subtract 8 from both sides of the equation: 2 x + 8 − 8 = − 10 − 8 , which simplifies to 2 x = − 18 .
Solving for x Finally, to solve for x , we divide both sides of the equation by 2: 2 2 x = 2 − 18 , which simplifies to x = − 9 .
Final Answer Therefore, the solution to the equation 5 x + 8 − 3 x = − 10 is x = − 9 .
Examples
Imagine you're managing a budget. You start with some money, spend some, and then receive more. Solving equations like this helps you figure out how much you initially had. For instance, if you start with an unknown amount, spend 3 x , receive $8, and end up with -$10, this equation helps you find the initial amount. This is a fundamental skill in personal finance and business management, ensuring you can track income, expenses, and overall financial health effectively.
