Question

35 points answer quickly please. 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+10) (c) 4x=2x+2x+5(x-x)

Answer 1

`\large \boxed{\mathrm{(a) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(b) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(c) \ All \ real \ numbers}}`

Explanation:

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

Expand brackets.

2x+4x-4=2+4x

Combine like terms.

6x-4=2+4x

Subtract 4x from both sides.

Add 4 to both sides.

2x=6

Divide both sides by 2.

x=3 (One solution)

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

Distribute negative sign.

25-x=15-3x-10

25-x=-3x+5

Add x and -5 to both sides.

20=-2x

Divide both sides by -2.

-10=x (One solution)

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

Solve for brackets.

4x=2x+2x+5(0)

4x=2x+2x

Combine like terms.

4x=4x

Divide both sides by 4.

x=x

All real numbers are solutions. (All real numbers)