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Algebraic Fractions, SMB-060

If  `3x-2=(x+1)/5`,  find  `x`.  (2 marks)

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`x=11/14`

Show Worked Solution
`3x-2` `= (x+1)/5`
 `5(3x-2)` `= x+1`
 `15x-10` `=x+1`
`14x` `=11`
`x` `=11/14`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-057

Find the value of  `r`  given  `5-(2r)/3 = 1`.  (2 marks)

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`r=6`

Show Worked Solution
`underbrace{5-(2r)/3}_text{Multiply × 3}` `= 1xx3`
`15-2r` `=3`
`2r` `= 12`
`r` `=6`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-056

If  `(n-5)/3 =4-n`,  find  `n`.  (2 marks)

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`n=17/4`

Show Worked Solution
`underbrace{(n-5)/3}_{text{Multiply × 3}}` `= underbrace{4-n}_{text{Multiply × 3}}`
 `n-5` `=3(4-n)`
 `n-5` `=12-3n`
`4n` `=17`
`n` `=17/4`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-055

If  `x-(x-3)/2 =4`,  find  `x`.  (2 marks)

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`x=5`

Show Worked Solution
`underbrace{x-(x-3)/2}_{text{Multiply × 2}}` `= 4`
 `2x-(x-3)` `= 8`
 `x+3` `=8`
`x` `=5`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-054

If  `(a-2)/5 =2`,  find  `a`.  (2 marks)

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`a=12`

Show Worked Solution
`(a-2)/5` `= 2`
 `a-2` `= 10`
 `a` `= 12`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-053

If  `(y-3)/2 =5-2y`,  find  `y`.  (2 marks)

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`y=13/5`

Show Worked Solution
`(y-3)/2` `= 5-2y`
 `y-3` `= 10-4y`
 `5y` `= 13`
`y` `=13/5`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-052

If  `(x-6)/3 =5`,  find  `x`.  (2 marks)

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`21`

Show Worked Solution
`(x-6)/3` `= 5`
 `x-6` `= 15`
 `x` `= 21`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Algebraic Fractions, SMB-051

Find the value of  `q`  given  `q/4-6 = -7`.  (2 marks)

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`-4`

Show Worked Solution
`q/4-6` `= -7`
`q/4` `= -1`
`:.q` `= -4`

Filed Under: Algebraic Fractions Tagged With: num-title-ct-corea, smc-4402-10-Single fraction

Functions, 2ADV F1 2021 HSC 11

Solve  `x+(x-1)/2 = 9`.  (2 marks)

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`19/3`

Show Worked Solution
`x+(x-1)/2` `=9`  
`2x + x-1` `=18`  
`3x` `=19`  
`x` `=19/3`  

Filed Under: Algebraic Fractions, Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11) Tagged With: 2adv-std2-common, Band 3, common-content, num-title-ct-corea, num-title-qs-hsc, smc-4402-10-Single fraction, smc-6213-10-Algebraic Fractions, smc-983-40-Algebraic Fractions

Algebra, STD2 A1 2017 HSC 9 MC

What is the value of  `x`  in the equation  `(5-x)/3 = 6`?

  1. `-13`
  2. `-3`
  3. `3`
  4. `13`
Show Answers Only

`A`

Show Worked Solution
`(5-x)/3` `= 6`
`5-x` `= 18`
`x` `= 5-18`
  `= -13`

`=>A`

Filed Under: Algebraic Fractions, Linear and Other Equations, Substitution and Other Equations (Std 1), Substitution and Other Equations (Std 2), Substitution and Other Equations (Std2-2027) Tagged With: Band 3, common-content, num-title-ct-corea, num-title-qs-hsc, smc-1116-30-Algebraic Fractions, smc-4402-10-Single fraction, smc-6234-30-Algebraic Fractions, smc-789-30-Algebraic Fractions

Algebra, STD2 A1 2014 HSC 26c

Solve the equation  `(5x + 1)/3-4 = 5-7x`.   (3 marks)

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 `x = 1`

Show Worked Solution
`(5x + 1)/3-4` `= 5-7x`
`5x + 1-3(4)` `= 3(5-7x)`
`5x + 1-12` `= 15-21x`
`26x` `= 26`
`:. x` `= 1`

Filed Under: Algebraic Fractions, Linear and Other Equations, Substitution and Other Equations (Std 1), Substitution and Other Equations (Std 2), Substitution and Other Equations (Std2-2027) Tagged With: Band 4, common-content, num-title-ct-corea, num-title-qs-hsc, smc-1116-30-Algebraic Fractions, smc-4402-10-Single fraction, smc-6234-30-Algebraic Fractions, smc-789-30-Algebraic Fractions

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