Question

Solve each given equation and show your work. Tell whether each equation has one solution, an infinite number of solutions, or no solution. Explain your answers.(a) 4 + 2( − 1) = 10 + 2

(b) 30 − = 10 − (6 + 10)
(c) 8x = 4x + 4x + 10(x − x)

Answer 1

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.

Final answers:

1. No solution (-2 ≠ 12)
2. No solution (30 ≠ -6)
3. Infinite number of solutions (8x = 8x -- resulting in same quotient)