Let's go through the steps to find the sum of the algebraic expressions -2.1x + 3.7 and 5 + 4.9x.
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Identify like terms.
- Like terms: -2.1x and 4.9x
- And 3.7 and 5
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Rewrite using properties of operations when necessary.
- Combine the like terms: \[ -2.1x + 4.9x + 3.7 + 5 \]
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Simplify.
- Combine the x terms: \[ (-2.1 + 4.9)x = 2.8x \]
- Combine the constant terms: \[ 3.7 + 5 = 8.7 \]
- Therefore, the simplified expression is: \[ 2.8x + 8.7 \]
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Check by substituting a value for x.
- For example, let’s substitute \( x = 1 \):
- Original expressions: \[ -2.1(1) + 3.7 = -2.1 + 3.7 = 1.6 \] \[ 5 + 4.9(1) = 5 + 4.9 = 9.9 \]
- Sum of original expressions: \[ 1.6 + 9.9 = 11.5 \]
- Using the simplified expression: \[ 2.8(1) + 8.7 = 2.8 + 8.7 = 11.5 \]
Thus, the sum of the algebraic expressions is confirmed, and we filled in the blanks as follows:
- -2.1x and 4.9x; 3.7 and 5
- (as shown above)
- 2.8x + 8.7
- substituting a value for x
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