Question

Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6

Answer 1

Option D:
`20 / 6-4` is the correct solution to the equation
`6(x+4)=20`

Option E:
`(1)/(6) (20-24)` is the correct solution to the equation
`6(x+4)=20`

Option F:
`(20-24) / 6` is the correct solution to the equation
`6(x+4)=20`

Step-by-step explanation:

The expression is
`6(x+4)=20`

Let us find the value of x.

`\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-(2)/(3)\end{aligned}`

Now, we shall find the expression that is equivalent to the value
`x=-(2)/(3)`

Option A:
`(20-4) / 6`

Simplifying the expression, we have,

`(16)/(6)=(8)/(3)`

Since,
`(8)/(3)` is not equivalent to
`x=-(2)/(3)`, the expression
`(20-4) / 6` is not equivalent to the equation
`6(x+4)=20`

Hence, Option A is not the correct answer.

Option B:
`16(20-4)`

Simplifying the expression, we have,

`16(16)=256`

Since, 256 is not equivalent to
`x=-(2)/(3)`, the expression
`16(20-4)` is not equivalent to the equation
`6(x+4)=20`

Hence, Option B is not the correct answer.

Option C:
`20-6-4`

Simplifying the expression, we have,

`20-10=10`

Since, 10 is not equivalent to
`x=-(2)/(3)`, the expression
`20-6-4` is not equivalent to the equation
`6(x+4)=20`

Hence, Option C is not the correct answer.

Option D:
`20 / 6-4`

Using PEMDAS and simplifying the expression, we have,

`$\begin{aligned}(20 / 6)-4 &=(10)/(3)-4 \\ &=(10-12)/(3) \\ &=-(2)/(3) \end{aligned}$`

Thus,
`-(2)/(3)` is equivalent to
`x=-(2)/(3)`, the expression
`20 / 6-4` is equivalent to the equation
`6(x+4)=20`

Hence, Option D is the correct answer.

Option E:
`(1)/(6) (20-24)`

Simplifying the expression, we have,

`$\begin{aligned} (1)/(6)(20-24) &=(1)/(6)(-4) \\ &=-(4)/(6) \\ &=-(2)/(3) \end{aligned}$`

Thus,
`-(2)/(3)` is equivalent to
`x=-(2)/(3)`, the expression
`(1)/(6) (20-24)` is equivalent to the equation
`6(x+4)=20`

Hence, Option E is the correct answer.

Option F:
`(20-24) / 6`

Simplifying the expression, we have,

`$\begin{aligned}(20-24) / 6 &=-(4)/(6) \\ &=-(2)/(3) \end{aligned}$`

Thus,
`-(2)/(3)` is equivalent to
`x=-(2)/(3)`, the expression
`(20-24) / 6` is equivalent to the equation
`6(x+4)=20`

Hence, Option F is the correct answer.