Find the value of x that satisfies the equation: \frac{x - 3}{4} + \frac{2x + 1}{3} = \fra… — Armed Services Vocational Aptitude Battery (ASVAB)

Find the value of $x$ that satisfies the equation:

\frac{x - 3}{4} + \frac{2x + 1}{3} = \frac{5x}{6}

Enter the exact value of $x$ .

Cevap: 5

Cevap

By finding the least common denominator (12) and multiplying every term by it, the fractions are cleanly eliminated. After applying the distributive property and combining like terms (

11x - 5 = 10x

), isolating the variable

x

yields exactly 5.

Adım Adım Çözüm

Multiply all terms by the least common denominator (12).

12 \left(\frac{x - 3}{4}\right) + 12 \left(\frac{2x + 1}{3}\right) = 12 \left(\frac{5x}{6}\right)

Multiplying by the LCD eliminates all fractions from the equation, simplifying further steps.

Simplify the resulting fractions.

3(x - 3) + 4(2x + 1) = 2(5x)

Dividing 12 by each respective denominator leaves an integer multiplier for the numerators.

Distribute the multipliers across the terms in the parentheses.

3x - 9 + 8x + 4 = 10x

The distributive property is required to remove the parentheses.

Combine like terms on the left side of the equation.

11x - 5 = 10x

Grouping

x

terms (

3x + 8x

) and constant terms (

-9 + 4

) simplifies the expression.

Isolate the variable

x

x = 5

Subtracting

10x

from both sides gives

x - 5 = 0

. Adding

5

to both sides results in

x = 5

Anahtar Kavram

Solving linear equations involving rational expressions by multiplying by a least common denominator.

Tahmini Süre:1m 30s

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