Solve for $x$.
$5(x-10)=30-15 x$
A. $x=1$
B. $x=4$
C. $x=5$
D. $x=8$
Answer (1)
Expand the left side of the equation: 5 ( x − 10 ) = 5 x − 50 .
Rewrite the equation: 5 x − 50 = 30 − 15 x .
Add 15 x to both sides: 20 x − 50 = 30 .
Add 50 to both sides and divide by 20 : x = 4 .
The solution is 4 .
Explanation
Understanding the Problem We are given the equation 5 ( x − 10 ) = 30 − 15 x and asked to solve for x . We need to find the value of x that satisfies this equation. The given options are x = 1 , x = 4 , x = 5 , and x = 8 .
Expanding the Equation First, let's expand the left side of the equation: 5 ( x − 10 ) = 5 x − 50 . So the equation becomes 5 x − 50 = 30 − 15 x .
Isolating x Next, we want to isolate x on one side of the equation. Add 15 x to both sides: 5 x − 50 + 15 x = 30 − 15 x + 15 x , which simplifies to 20 x − 50 = 30 .
Further Isolating x Now, add 50 to both sides of the equation: 20 x − 50 + 50 = 30 + 50 , which simplifies to 20 x = 80 .
Solving for x Finally, divide both sides by 20 : 20 20 x = 20 80 , which simplifies to x = 4 .
Final Answer Therefore, the solution to the equation is x = 4 .
Examples
Imagine you're buying concert tickets online. The total cost is calculated as a base fee plus a service charge per ticket. If the equation 5 ( x − 10 ) = 30 − 15 x represents the relationship between the number of tickets you buy ( x ) and the total cost, solving for x helps you determine how many tickets you can buy within a certain budget. Understanding how to solve such equations is useful in managing personal finances and making informed purchasing decisions.
