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.
Similar Questions
Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
- The product of two positive numbers is 1445. If the first number is five times of the second number, then the sum of the two numbers is:
- The value of $x$ satisfying the equation $x^2 + a^2 = (b - x)^2$ is:
- Out of four consecutive numbers, the sum of the first two numbers is equal to the fourth number. What is half of the sum of the four numbers?
- If $p = 5 - 2\sqrt{6}$, then find the value of $p^2 + \frac{1}{p^2}$
- Which of the following number, when added to itself 14 times gives 135 as result?
- Simplify $x(7x - 2) + 5(x^2 - 3) + 13$.
- What is the number of all positive solutions of the equation $|x \times 1| = 0$ ?
- If $a + b = 5$ and $ab = 13$, then what will be the value of $a^3 + b^3$?
- The value of $p^2 - 7p + 12$ at $p = 3$ is:
Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
