Question

Solve each given equation and show your work. Tell weather each equation has one solution, an infinite number of solutions, or no solution. Explain your answer.
(a) 4x + 2(x-1) =10 + 2x
(b) 30- x =10-(6x +10)
(c) 8x = 4x + 4x +10 (x-x)
30 POINTS !!!!

Answer 1

Hello!

To solve algebraic equations, you need to SADMEP it. SADMEP is only used to solve these equations, and it is an acronym for subtraction, addition, division, multiplication, exponents, and parentheses. The goal here is to get x on one side of the equation.

(a) 4x + 2(x - 1) = 10 + 2x (use the distributive property)

4x + 2x - 2 = 10 + 2x (add alike terms)

6x - 2 = 10 + 2x (subtract 2x from both sides)

4x - 2 = 10 (add 2 to both sides)

4x = 12 (divide both sides by 4)

x = 3

This equation has one solution because if you substitute 3 for x into the original equation, then both sides of the equation will be equal.

(b) 30 - x = 10 + -1(6x + 10) (use the distributive property)

30 - x = 10 + -6x - 10 (simplify)

30 - x = -6x (add x to both sides)

30 = -5x (divide both sides by -5)

x = -6

This equation has one solution because if you substitute x = -6 into the given equation, then the left and right side of the equation will be equivalent to each other.

(c) 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 number into the given equation, both sides of the equation will be equal.