Solve for $x$.
$\begin{array}{c}
5(12-2 x)=-10 \\
x=[?]
\end{array}$
Answer (1)
Distribute the 5: 5 × 12 − 5 × 2 x = − 10 .
Simplify: 60 − 10 x = − 10 .
Subtract 60 from both sides: − 10 x = − 70 .
Divide by -10 to solve for x: x = 7 .
Explanation
Problem Setup We are given the equation 5 ( 12 − 2 x ) = − 10 and we want to solve for x .
Distribute First, distribute the 5 on the left side of the equation: 5 × 12 − 5 × 2 x = − 10
Simplify Simplify the equation: 60 − 10 x = − 10
Isolate x term Subtract 60 from both sides of the equation: − 10 x = − 10 − 60
Simplify Simplify: − 10 x = − 70
Solve for x Divide both sides by − 10 : x = − 10 − 70
Final Answer Simplify to find the value of x : x = 7
Examples
Imagine you're buying concert tickets online. The base price for each ticket is $12, but there's a discount of $2 for each ticket you buy. If the total cost for 5 tickets is supposed to be -$10 (a refund), this equation helps you find out how many tickets were actually refunded. Solving such equations is useful in determining quantities, prices, or any variable in real-world scenarios where there are discounts or refunds involved.
