$2(2 x+3)-6=16$
Distribute (to get rid of parentheses) | |
Combine any Like Terms | |
Undo addition or subtraction first | |
Undo multiplication or division next | |
The given equation is \(2(2x + 3) - 6 = 16\). Our goal is to solve for the variable \(x\). This equation requires applying the distributive property, simplifying by combining constant terms, and finally isolating the variable \(x\) using inverse operations.
First, we apply the distributive property by multiplying the 2 by both terms inside the parentheses:
\[2(2x) + 2(3) - 6 = 16\]
\[4x + 6 - 6 = 16\]
This expands the equation, preparing it for simplification.
Next, we combine the constant terms on the left side of the equation. Since \(6 - 6 = 0\), the equation simplifies significantly:
\[4x + 0 = 16\]
\[4x = 16\]
This leaves us with a simple equation where \(x\) is being multiplied by 4.
To isolate \(x\), we divide both sides of the equation by 4:
\[\frac{4x}{4} = \frac{16}{4}\]
\[x = 4\]
The value of \(x\) that satisfies the original equation is 4.
Solving linear equations like this is a fundamental skill used in everyday life, such as when calculating budget allocations or adjusting recipes. For example, if you are planning to buy a certain number of items, where you have a set initial amount and a fixed discount, you can use an algebraic equation to determine how many items you can afford. By mastering these techniques, you gain the ability to manage resources effectively and solve practical problems efficiently.