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Difficulty: HardSolving One-Variable Linear Equations

Determine the numerical value of the variable xx that satisfies the algebraic equation below.

Answer:38(16x−24)+5=−2(2x−1)+4x+6 \frac{3}{8}(16x - 24) + 5 = -2(2x - 1) + 4x + 6

x=x = 【2】

Answer

The value of x that satisfies the equation is 2.
By successfully applying the distributive property to both sides of the equation, the expression simplifies to 6x - 9 + 5 = -4x + 2 + 4x + 6. Combining like terms reduces this to 6x - 4 = 8. Adding 4 to both sides yields 6x = 12, which gives exactly 2.

Step-by-Step Solution

1
Distribute the fraction on the left side and the negative integer on the right side.
6x−9+5=−4x+2+4x+6 6x - 9 + 5 = -4x + 2 + 4x + 6
Applying the distributive property removes the grouping parentheses, which is necessary before combining any terms.
2
Combine the constant terms on the left side and the like terms on the right side.
6x−4=8 6x - 4 = 8
Simplifying both sides of the equation by grouping like terms makes it straightforward to isolate the variable. The -4x and +4x cancel each other out.
3
Isolate the term containing the variable by adding 4 to both sides of the equation.
6x=12 6x = 12
Using the addition property of equality maintains the balance while moving constants to one side.
4
Divide both sides by 6 to solve for x.
x=2 x = 2
Dividing by the coefficient of x isolates the variable completely and provides the final solution.

Key Concept

Solving multi-step linear equations involving fractional distribution and combining like terms across both sides of the equals sign.
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Topics

Solving One-Variable Linear Equations

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