Hello!
To solve algebraic equations, we need to use SADMEP. SADMEP is only used to solve algebraic equations. It is an acronym for subtract, addition, division, multiplication, exponents, and parentheses.
(a) 2x + 4(x - 1) = 2 + 4x (use the distributive property)
2x + 4x - 4 = 2 + 4x (simplify alike terms)
6x - 4 = 2 + 4x (subtract 4x from both sides)
2x - 4 = 2 (add 4 to both sides)
2x = 6 (divide both sides by 2)
x = 3
This equation has one solution because if you <u>substitute x = 3</u> into the original equation, <u>both sides will be equal</u> to each other.
(b) 25 - x = 15 + -1(3x + 10) (use the distributive property)
25 - x = 15 - 3x - 10 (add)
25 - x = -3x + 5 (subtract 5 from both sides)
20 - x = -3x (add x to both sides)
20 = -2x (divide both sides by -2)
x = -10
This equation has one solution because if you <u>substitute x = -10</u> into the original equation, then <u>both sides of the equation will be equivalent</u>.
(c) 4x = 2x + 2x + 5(x - x) (simplify - add and subtract)
4x = 4x + 5(0) (multiply)
4x = 4x
This equation has an infinite number of solutions because if you substitute <u>any number</u> into the equation, then <u>both sides will be equal</u> to each other <u>no matter what number</u> is used.