Questions: Solve the equation. Express numbers as integers or simplified fractions. 4(a-4)=-7a-17+11a - The solution set is .

Solve the equation. Express numbers as integers or simplified fractions. 4(a-4)=-7a-17+11a - The solution set is .
Transcript text: Solve the equation. Express numbers as integers or simplified fractions. \[ 4(a-4)=-7 a-17+11 a \] - The solution set is $\square$ .
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Solution

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Solution Steps

To solve the equation \(4(a-4)=-7a-17+11a\), we need to simplify and solve for \(a\). Here are the high-level steps:

  1. Distribute the 4 on the left side.
  2. Combine like terms on both sides.
  3. Isolate the variable \(a\) to solve for it.
Step 1: Distribute the 4 on the left side

First, we distribute the 4 on the left side of the equation: \[ 4(a - 4) = 4a - 16 \] So the equation becomes: \[ 4a - 16 = -7a - 17 + 11a \]

Step 2: Combine like terms on the right side

Next, we combine like terms on the right side of the equation: \[ -7a + 11a = 4a \] So the equation simplifies to: \[ 4a - 16 = 4a - 17 \]

Step 3: Isolate the variable \(a\)

To isolate \(a\), we subtract \(4a\) from both sides of the equation: \[ 4a - 16 - 4a = 4a - 17 - 4a \] This simplifies to: \[ -16 = -17 \]

Step 4: Analyze the result

The equation \(-16 = -17\) is a contradiction, which means there is no value of \(a\) that satisfies the equation.

Final Answer

The solution set is \(\boxed{\text{no solution}}\).

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