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Zorluk: OrtaLinear Equations in One Variable

If 14(8x−12)−23(3−6x)=13\frac{1}{4}(8x - 12) - \frac{2}{3}(3 - 6x) = 13, what is the value of 3x−23x - 2?

  1. A
    2
  2. B
    3
  3. 7Cevap
  4. D
    -29

Cevap

7
Distributing the coefficients yields 14(8x−12)=2x−3\frac{1}{4}(8x - 12) = 2x - 3 and −23(3−6x)=−2+4x-\frac{2}{3}(3 - 6x) = -2 + 4x. Combining these terms gives the simplified equation 6x−5=136x - 5 = 13. Adding 55 to both sides yields 6x=186x = 18, and dividing by 66 gives x=3x = 3. Substituting x=3x = 3 into the expression 3x−23x - 2 results in 3(3)−2=73(3) - 2 = 7.

Adım Adım Çözüm

1
Distribute the fraction coefficients to the terms inside the parentheses.
14(8x−12)=2x−3\frac{1}{4}(8x - 12) = 2x - 3 and −23(3−6x)=−2+4x-\frac{2}{3}(3 - 6x) = -2 + 4x.
This simplifies the equation by removing the parentheses.
2
Combine like terms on the left side of the equation.
(2x−3)+(−2+4x)=6x−5(2x - 3) + (-2 + 4x) = 6x - 5, transforming the equation to 6x−5=136x - 5 = 13.
Grouping the variable terms and constant terms is necessary to isolate the variable.
3
Isolate the variable by adding 5 to both sides and dividing by 6.
6x=18⇒x=36x = 18 \Rightarrow x = 3.
This determines the value of the variable.
4
Substitute the value of xx into the expression 3x−23x - 2.
3(3)−2=73(3) - 2 = 7.
The question asks for the value of the expression 3x−23x - 2, not the value of xx itself.

Anahtar Kavram

Linear Equations in One Variable

Alternatif Yöntem

An alternative method is to multiply both sides of the equation by the least common multiple of the denominators 44 and 33, which is 1212. Multiplying the entire equation by 1212 yields 3(8x−12)−8(3−6x)=1563(8x - 12) - 8(3 - 6x) = 156. Distributing gives 24x−36−24+48x=15624x - 36 - 24 + 48x = 156, which simplifies to 72x−60=15672x - 60 = 156. Adding 6060 gives 72x=21672x = 216, so x=3x = 3. Substituting x=3x = 3 into 3x−23x - 2 gives 77.
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Konular

Linear Equations in One Variable

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