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) 2x + 4(x-1) = 2 + 4x
(B) 25- x = 15 - (3x + x)
(C) 4x = 2x + 2x + 5(x-4)

Answer 1

(a) 2x+4(x-1)=2

2x+4x-4=2---- Distrubution of 4(x-1)

6x-4=2---- Combining like terms

6x=6---- Making -4 equal 0 by adding +4 to both sides

x=1---- Divide the coefficiant (6)

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

25-x=15-3x-10----Distribute the -1

25-x=5-3x---- Combine like terms

25=5-2x---- Make -x equal 0 by adding +x to both sides

20=-2x---- Make 5 equal zero by subtracting 5 (or adding -5) to both sides

-10=x---- Divide by the coefficiant (-2)

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

4x=2x+2x+5(0)---- Distribute. Alright this might look hard but realy it is 1x-1x so the answer is 0

4x=2x+2x---- 5 times 0 is 0

4x=4x---- Combine like terms

x=x ---- divide by the coefficiant