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Zorluk: ZorLinear Equations in One Variable
In the equation below, xx is a real number.
56(3x−4)−38(4x−12)=14(2x+6)\frac{5}{6}(3x - 4) - \frac{3}{8}(4x - 12) = \frac{1}{4}(2x + 6)
What is the value of 6x−56x - 5?
  1. A
    107107
  2. −1-1Cevap
  3. C
    77
  4. D
    −21-21

Cevap

−1-1
The correct answer is −1-1. First, distribute the fractions across the parentheses on both sides of the equation:
56(3x−4)−38(4x−12)=14(2x+6)\frac{5}{6}(3x - 4) - \frac{3}{8}(4x - 12) = \frac{1}{4}(2x + 6)
52x−103−32x+92=12x+32\frac{5}{2}x - \frac{10}{3} - \frac{3}{2}x + \frac{9}{2} = \frac{1}{2}x + \frac{3}{2}
Combine the like terms on the left side:
(52x−32x)+(−103+92)=12x+32\left(\frac{5}{2}x - \frac{3}{2}x\right) + \left(-\frac{10}{3} + \frac{9}{2}\right) = \frac{1}{2}x + \frac{3}{2}
x+76=12x+32x + \frac{7}{6} = \frac{1}{2}x + \frac{3}{2}
Subtract 12x\frac{1}{2}x from both sides:
12x+76=32\frac{1}{2}x + \frac{7}{6} = \frac{3}{2}
Subtract 76\frac{7}{6} from both sides:
12x=96−76=26=13\frac{1}{2}x = \frac{9}{6} - \frac{7}{6} = \frac{2}{6} = \frac{1}{3}
Multiply by 22 to solve for xx:
x=23x = \frac{2}{3}
Finally, substitute x=23x = \frac{2}{3} into the expression 6x−56x - 5:
6(23)−5=4−5=−16\left(\frac{2}{3}\right) - 5 = 4 - 5 = -1

Adım Adım Çözüm

1
Distribute the coefficients to the terms within the parentheses on both sides of the equation.
52x−103−32x+92=12x+32\frac{5}{2}x - \frac{10}{3} - \frac{3}{2}x + \frac{9}{2} = \frac{1}{2}x + \frac{3}{2}
To simplify the linear equation, parenthetical expressions must be expanded.
2
Combine like terms on the left side of the equation.
x+76=12x+32x + \frac{7}{6} = \frac{1}{2}x + \frac{3}{2}
Grouping the variable terms (xx) and constant terms simplifies the equation prior to isolation.
3
Isolate the variable term on one side of the equation by subtracting 12x\frac{1}{2}x and 76\frac{7}{6} from both sides.
12x=13\frac{1}{2}x = \frac{1}{3}
This isolates the variable xx on the left side and the constants on the right side.
4
Solve for xx by multiplying both sides by 22.
x=23x = \frac{2}{3}
Multiplying by the reciprocal of the coefficient of xx gives the value of xx.
5
Substitute the value of xx into the expression 6x−56x - 5.
−1-1
The question asks for the value of the expression 6x−56x - 5, not the variable xx.

Anahtar Kavram

Solving multi-step linear equations in one variable containing fractions and parentheses.
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Konular

Linear Equations in One Variable

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