Question

Solve each equation. (Hint: Leave your answers as integers or fractions. Write fractions in the form 1/2)

1. 8x=2/3; x=?
2. 1 1/2=2x; x=?
3. 5x=2/7; x=?
4. 1/4x= 5; x=?
5.1/5= 2/3x; x=?

Answer 1

[1]
`x=(1)/(12)`

[2]
`x=(3)/(4)`

[3]
`x=(2)/(35)`

[4]
`x=20`

[5]
`x=(3)/(10)`

Explanation:

[1]
`8x=(2)/(3)`

`\mathrm{Divide\:both\:sides\:by\:}8`

`(8x)/(8)=((2)/(3))/(8)`

`\mathrm{Simplify}`

`x=(1)/(12)`

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[2]
`1\:(1)/(2)=2x`

`(3)/(2)=2x`

`\mathrm{Divide\:both\:sides\:by\:}2`

`(2x)/(2)=((3)/(2))/(2)`

`\mathrm{Simplify}`

`x=(3)/(4)`

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[3]
`5x=(2)/(7)`

`\mathrm{Divide\:both\:sides\:by\:}5`

`(5x)/(5)=((2)/(7))/(5)`

`\mathrm{Simplify}`

`x=(2)/(35)`

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[4]
`(1)/(4)x=\:5`

`\mathrm{Multiply\:both\:sides\:by\:}4`

`4\cdot (1)/(4)x=5\cdot \:4`

`\mathrm{Simplify}`

`x=20`

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[5]
`(1)/(5)=\:(2)/(3)x`

`\mathrm{Multiply\:both\:sides\:by\:}3`

`3\cdot (2)/(3)x=(1\cdot \:3)/(5)`

`\mathrm{Simplify}`

`2x=(3)/(5)`

`\mathrm{Divide\:both\:sides\:by\:}2`

`(2x)/(2)=((3)/(5))/(2)`

`\mathrm{Simplify}`

`x=(3)/(10)`

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~Lenvy~

Answer 2

Explanation:

1: 8*1/12=2/3 1/12

2: 1 1/2 = 2 3/4 3/4

3: 5*2/3=2/7 2/35

4: 1/4*20 = 5 20

5: 1/5 = 2/3* 3/10 3/10