The given equations: 5(x - 2) = 5x - 7, - 3(x - 4) = - 3x + 12, 4(x + 1) = 3x + 4, 2(x - 3) = 2x - 6, 6(x + 5) = 6x + 11, have no solution, infinitely many solutions, one solution, one solution, and no solution respectively.
"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign."
Given equations are:
1. 5(x - 2) = 5x - 7
⇒ 5x - 10 = 5x - 7
Therefore, this equation has no solution.
2. - 3(x - 4) = - 3x + 12
⇒ - 3x + 12 = - 3x + 12
Therefore, this equation has infinitely many solutions.
3. 4(x + 1) = 3x + 4
⇒ 4x + 4 = 3x + 4
⇒ x = 0
Therefore, this equation has only one solution.
4. - 2(x - 3) = 2x - 6
⇒ - 2x + 6 = 2x - 6
⇒ 4x = 12
⇒ x = 3
Therefore, this equation has only one solution.
5. 6(x + 5) = 6x + 11
⇒ 6x + 30 = 6x + 11
Therefore, this equation has no solution.
Learn more about an equation here: https://brainly.com/question/12283977
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