By the knowledge and application of algebraic definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)
How to solve an algebraic equation
In this question we have an equation that can be solved by algebraic definitions and theorems, whose objective consists in clearing the variable x. Now we proceed to solve the equation for x:
- - 10 · x + 1 + 7 · x = 37 Given
- (- 10 · x + 7 · x) + 1 = 37 Associative property
- -3 · x + 1 = 37 Distributive property/Definition of subtraction
- - 3 · x = 36 Compatibility with addition/Definition of subtraction
- x = 12 Compatibility with multiplication/a/(-b) = -a/b/Definition of division/Result
By the knowledge and application of algebraic definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)
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