Question

a. 10x-6=44b. (x+3)-15=48c. 4(x+6)-10=26d. 3(x+3)-15=48e.Which two equations have the same solution set? Write a sentence explaining how the properties of equality can be used to determine the pair without having to find the solution set for each.

Answer 1

a.

`\begin{gathered} 10x-6=44 \\ 10x=44+6 \\ 10x=50 \\ x=(50)/(10) \\ x=5 \end{gathered}`

b.

`\begin{gathered} 9(x+3)-15=48 \\ 9x+27-15=48 \\ 9x+12=48 \\ 9x=36 \\ x=(36)/(9) \\ x=4 \end{gathered}`

c.

`\begin{gathered} 4(x+6)-10=26 \\ 4x+24-10=26 \\ 4x+14=26 \\ 4x=26-14 \\ 4x=12 \\ x=(12)/(4) \\ x=3 \end{gathered}`

d.

`\begin{gathered} 3(x+3)-15=48 \\ 3x+9-15=48 \\ 3x-6=48 \\ 3x=48+6 \\ 3x=54 \\ x=(54)/(3) \\ x=18 \end{gathered}`

The answer in set notation

`x=\mleft\lbrace5,4,3,18\mright\rbrace`

e. Equation b and Equation d have the same solution set . Both of the equations is equals to 48.