Solve for $x$ using the distributive property.
$\begin{array}{l}
2(5+x)=40 \
{[?]+\square x }=40 \
(2 \cdot 5)
\end{array}$
Hint: Multiply both terms inside the parentheses with the number on the outside.
Answer (2)
Apply the distributive property: 2 ( 5 + x ) = 10 + 2 x .
Rewrite the equation: 10 + 2 x = 40 .
Subtract 10 from both sides: 2 x = 30 .
Divide by 2 to solve for x : x = 15 .
Explanation
Understanding the Problem We are given the equation 2 ( 5 + x ) = 40 and we need to solve for x using the distributive property. The distributive property states that a ( b + c ) = ab + a c .
Applying the Distributive Property First, we apply the distributive property to expand the left side of the equation: 2 ( 5 + x ) = 2 × 5 + 2 × x
Simplifying the Equation Now we simplify the equation: 10 + 2 x = 40
Isolating the x term Next, we subtract 10 from both sides of the equation to isolate the term with x : 10 + 2 x − 10 = 40 − 10 2 x = 30
Solving for x Finally, we divide both sides by 2 to solve for x : 2 2 x = 2 30 x = 15
Examples
Imagine you're buying tickets for a school play. Each ticket costs $5, and you're also buying some extra programs for $2 each. If you buy 2 tickets and some programs, and your total cost is $40, this problem helps you figure out how many programs you bought. The distributive property helps break down the cost and solve for the unknown number of programs.
To solve 2 ( 5 + x ) = 40 , we use the distributive property to rewrite it as 10 + 2 x = 40 . By isolating x , we find x = 15 . This demonstrates how to expand and solve equations effectively.
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