Hello!
To solve algebraic equations, we need to use SADMEP. SADMEP acts like PEMDAS and is subtract, addition, division, multiplication, exponents and parentheses. If there are no variables, it is a regular equation, and can be simplified using PEMDAS.
(a) 4 + 2(-1) = 10 + 2 (multiply)
4 + -2 = 10 + 2 (add)
2 = 12
This equation has no solutions because -2 is not equal to 12.
(b) 30 = 10 + -1(6 + 10) (simplify)
30 = 10 + -1(16) (multiply)
30 = 10 + -16 (add)
30 = -6
This equation has no solutions because 30 is not equal to -6.
(c) 8x = 4x + 4x + 10(x - x) (simplify alike terms)
8x = 8x + 10(0) (multiply)
8x = 8x
This equation has an infinite number of solutions because another number substitute into x will result in the same solution on both sides of the equation.
<u>Final answers</u>:
- No solution (-2 ≠ 12)
- No solution (30 ≠ -6)
- Infinite number of solutions (8x = 8x -- resulting in same quotient)
