Question

Observe each equation and determine the number of solutions a) 8x- 9 = -4x + 15b) 6 - 2h = -2h - 4c) 1/2n + 3/5 = 3/5 + 1/2nd) 0.72 - 3w = 5w + 0.28

Answer 1

Solving each equation, we have:

a)

`\begin{gathered} 8x-9=-4x+15 \\ 8x+4x=15+9 \\ 12x=24 \\ x=2 \end{gathered}`

This equation has one solution.

b)

`\begin{gathered} 6-2h=-2h-4 \\ 6=-4 \end{gathered}`

The sentence is false, therefore the equation has no solution.

c)

`\begin{gathered} (1)/(2)n+(3)/(5)=(3)/(5)+(1)/(2)n \\ 0=0 \end{gathered}`

The sentence is true, therefore the equation has infinitely many solutions.

d)

`\begin{gathered} 0.72-3w=5w+0.28_{} \\ 5w+3w=0.72-0.28 \\ 8w=0.44 \\ w=(0.44)/(8)=0.055 \end{gathered}`

This equation has one solution.