Questions: Solve for a. 4(a+2)=8+4a all real numbers -1 no solution -2

Solve for a. 4(a+2)=8+4a all real numbers -1 no solution -2
Transcript text: Solve for a. \[ 4(a+2)=8+4 a \] all real numbers $-1$ no solution $-2$
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Solution

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Solution Steps

To solve the equation \(4(a+2) = 8 + 4a\), we first expand the left side of the equation. Then, we simplify both sides and isolate the variable \(a\) to find its value.

Step 1: Expand the Equation

We start with the equation: \[ 4(a + 2) = 8 + 4a \] Expanding the left side gives: \[ 4a + 8 = 8 + 4a \]

Step 2: Simplify the Equation

Next, we simplify both sides. Subtract \(4a\) from both sides: \[ 4a + 8 - 4a = 8 + 4a - 4a \] This simplifies to: \[ 8 = 8 \]

Step 3: Analyze the Result

The equation \(8 = 8\) is always true, which means that there are infinitely many solutions for \(a\). Thus, \(a\) can be any real number.

Final Answer

The answer is that there are infinitely many solutions, so we can say: \[ \boxed{a \in \mathbb{R}} \]

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