Question

2. 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 is an acronym used only solve for x in algebraic equations. SADMEP is expanded to be: subtraction, addition, division, multiplication, exponents, and parentheses.

(a) 4 + 2(-1) = 10 + 2 (multiply)

4 + -2 = 10 + 2 (add)

2 = 12

This equation has no solutions because 2 is never equal to 12.

(b) 30 = 10 - (6 + 10) (simplify the parentheses)

30 = 10 + -1(16) (multiply)

30 = 10 - 16 (simplify)

30 = -6

This equation has no solutions because 30 and -6 is never equal to each other.

(c) 8x = 4x + 4x + 10(x - x)

8x = 4x + 4x + 10(x - x) (simplify [add and subtract])

8x = 8x + 10(0) (multiply)

8x = 8x  

This equation has an infinite number of solutions because if you substitute any value into the original equation, both sides of the equation will be always equal.