Question

Which expressions are equivalent to05-3x+35-12Ox+4701x+35-12x+1205(x)+(5) (7)-(3)(x) + (3)(4)01x+35-1-x-125(x+7)-3(x-4)? Select three options.

Answer 1

Step-by-step explanation:

Given:

`5((1)/(3)x+7)\text{ - 3\lparen}(1)/(2)x\text{ - 4\rparen}`

To find:

Three equivalent expressions

To determine the expressions, we will expand the parenthesis:

`=\text{ }5((1)/(3)x)+5(7)\text{ - 3\lparen}(1)/(2)x)\text{ - 3\lparen-4\rparen \lparen4th option\rparen}`
`\begin{gathered} Next,\text{ we will simplify:} \\ $$mu\text{ltiplication of same signs give positive sign}$$ \\ $$m\text{ ultiplication of opposite signs give negative sign}$$ \\ (5)/(3)x\text{ + 35 - }(3)/(2)x\text{ + 12} \\ \\ To\text{ improper fraction:} \\ =1(2)/(3)x\text{ + 35 -1}(1)/(2)x\text{ + 12 \lparen3rd option\rparen} \end{gathered}`
`\begin{gathered} collect\text{ like terms:} \\ 1(2)/(3)x\text{ - 1}(1)/(2)x\text{ + 35 + 12} \\ \\ LCMof\text{ the fraction = 6} \\ 1(2)/(3)x\text{ - 1}(1)/(2)x=\text{ }\frac{4x\text{ - 3x}}{6}\text{ \lparen whoe number cancel out\rparen} \\ =\text{ }(x)/(6) \\ \\ 1(2)/(3)x\text{ - 1}(1)/(2)x\text{ + 35 + 12 = }(x)/(6)\text{ + 47} \\ \\ =\text{ }(1)/(6)x\text{ + 47 \lparen2nd option\rparen} \end{gathered}`