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Zorluk: OrtaLinear Equations in One Variable

If 3(x−2)−4(2−x)=12(6x−4)+13(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1, what is the value of 2x−32x - 3?

  1. A
    −192-\frac{19}{2}
  2. 72\frac{7}{2}Cevap
  3. C
    92\frac{9}{2}
  4. D
    134\frac{13}{4}

Cevap

The value of the expression is 72\frac{7}{2}.
The correct answer is 72\frac{7}{2}. Distributing the constants on both sides of the equation 3(x−2)−4(2−x)=12(6x−4)+13(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1 yields 3x−6−8+4x=3x−2+13x - 6 - 8 + 4x = 3x - 2 + 1. Combining like terms on both sides gives 7x−14=3x−17x - 14 = 3x - 1. Subtracting 3x3x from both sides and adding 1414 to both sides results in 4x=134x = 13, which simplifies to x=134x = \frac{13}{4}. Substituting this value into 2x−32x - 3 gives 2(134)−3=132−3=722\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}.

Adım Adım Çözüm

1
Distribute the constants on both sides of the equation.
3x−6−8+4x=3x−2+13x - 6 - 8 + 4x = 3x - 2 + 1
To simplify the linear terms and constants before isolating the variable.
2
Combine like terms on both sides of the equation.
7x−14=3x−17x - 14 = 3x - 1
To reduce the equation to a simpler form with one variable term and one constant term on each side.
3
Isolate the variable term by subtracting 3x3x from both sides and adding 1414 to both sides.
4x=134x = 13
To group all variable terms on one side and constant terms on the other.
4
Solve for xx by dividing both sides by 44.
x=134x = \frac{13}{4}
To isolate the variable xx.
5
Substitute the value of xx into the expression 2x−32x - 3.
2(134)−3=132−3=722\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}
To calculate the final value requested by the question.

Anahtar Kavram

Solving linear equations in one variable by distributing terms, combining like terms, isolating the variable, and evaluating algebraic expressions.
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Konular

Linear Equations in One Variable

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