Questions: Simplify the expression by combining like terms: 10a + 7 + 5a - 2 + 7a - 4

Simplify the expression by combining like terms: 10a + 7 + 5a - 2 + 7a - 4
Transcript text: Simplify the expression by combining like terms: $10 a+7+5 a-2+7 a-4$
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Solution

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Solution Steps

Step 1: Identify like terms

The expression is \(10a + 7 + 5a - 2 + 7a - 4\). The like terms are:

  • \(10a\), \(5a\), and \(7a\) (all terms with \(a\))
  • \(7\), \(-2\), and \(-4\) (constant terms)
Step 2: Combine the like terms with \(a\)

Add the coefficients of the terms with \(a\): \[ 10a + 5a + 7a = (10 + 5 + 7)a = 22a \]

Step 3: Combine the constant terms

Add the constant terms: \[ 7 - 2 - 4 = 1 \]

Step 4: Write the simplified expression

Combine the results from Step 2 and Step 3: \[ 22a + 1 \]

Final Answer

\(\boxed{22a + 1}\)

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