Multi-Step Equations with Like Terms
Key Questions
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You combine like terms by variable(s) and exponent(s).
The variables and exponent must match in order to combine.
So take
#x^2 + x# . Variables (x and x) match, but exponents (2 and 1) do not, so you cannot combineTake
#x^2 + y^2# . Exponents (2 and 2) match, but variables (x and y) do not.Now, take
#3x^2 + 5x^2# These CAN be combine since the variable of x and power of 2 match.So we have
#3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2# -
Example . Solve: 3x + 4m - 5 = 2x - 2m + 7.
First, combine x terms: -2x = - 2x
x + 4m - 5 = -2m + 7
Next, combine m terms and constants
- 4m + 5 = - 4m + 5
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x = -6m + 12