Solving the Linear Equation for Variable x
This section details the steps to find the value of the variable x in the given linear equation.
Equation Analysis
The equation provided is:
$3(5x + 2) - 4 = 2(1 - 4x)$
Step-by-Step Solution
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Distribute: Apply the distributive property on both sides of the equation.
- Left side: $3 \times 5x + 3 \times 2 - 4 = 15x + 6 - 4$
- Right side: $2 \times 1 - 2 \times 4x = 2 - 8x$
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Simplify: Combine constant terms on the left side.
- $15x + 2 = 2 - 8x$
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Isolate Variable Terms: Move all terms containing x to one side and constants to the other. Add $8x$ to both sides.
- $15x + 8x + 2 = 2 - 8x + 8x$
- $23x + 2 = 2$
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Isolate Constant Terms: Subtract 2 from both sides to isolate the term with x.
- $23x + 2 - 2 = 2 - 2$
- $23x = 0$
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Solve for x: Divide both sides by the coefficient of x, which is 23.
- $x = \frac{0}{23}$
- $x = 0$
Conclusion
The value of the variable x that satisfies the equation $3(5x + 2) - 4 = 2(1 - 4x)$ is 0.
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