Question

Solve each given equation and show your work. tell whether each equation has one solution and infinite number of solutions or no solution. Explain your work
(a) 2x + 4 (x - 1) = 2 + 4x

(b) 25 - x = 15 - (3x + 10)

(c) 4 x = 2x + 2 x + 5 (x - x)

Answer 1

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 substitute x = 3 into the original equation, both sides will be equal 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 substitute x = -10 into the original equation, then both sides of the equation will be equivalent.

(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 any number into the equation, then both sides will be equal to each other no matter what number is used.