Find $x$ in $10-2 x=-18$
Answer (1)
Subtract 10 from both sides of the equation: − 2 x = − 28 .
Divide both sides by -2: x = − 2 − 28 .
Simplify to find the value of x .
The solution to the equation is 14 .
Explanation
Understanding the Problem We are given the equation 10 − 2 x = − 18 and our goal is to find the value of x that satisfies this equation.
Isolating the x term First, we want to isolate the term with x on one side of the equation. To do this, we subtract 10 from both sides of the equation:
10 − 2 x − 10 = − 18 − 10
Simplifying the equation Simplifying both sides, we get:
− 2 x = − 28
Solving for x Now, we want to solve for x by dividing both sides of the equation by -2:
− 2 − 2 x = − 2 − 28
Finding the value of x Simplifying, we find the value of x :
x = 14
So, the solution to the equation is x = 14 .
Examples
In real life, solving linear equations like this can help you determine how many items you need to sell to reach a certain profit goal. For example, if you know your fixed costs are $10 and you make $2 profit on each item you sell, you can use the equation 10 − 2 x = − 18 to find out how many items you need to sell to have a total profit of $18. In this case, x represents the number of items you need to sell, and solving the equation gives you the answer.
