Solve each equation for x. 3x=(2x-1)(m+4)

Verified step by step guidance

Start with the given equation: \$3x = (2x - 1)(m + 4)$.

Apply the distributive property to the right-hand side: multiply each term inside the parentheses by $(m + 4)$, resulting in \$3x = 2x(m + 4) - 1(m + 4)$.

Rewrite the right-hand side explicitly as $3x = 2x \cdot m + 2x \cdot 4 - (m + 4)$, which simplifies to \$3x = 2xm + 8x - m - 4$.

Collect all terms involving $x$ on one side and constants on the other side. For example, subtract \$2xm$ and $8x$ from both sides to get $3x - 2xm - 8x = -m - 4$.

Factor out $x$ on the left side: $x(3 - 2m - 8) = -m - 4$. Then, solve for $x$ by dividing both sides by $(3 - 2m - 8)$, giving $x = \frac{-m - 4}{3 - 2m - 8}$.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. In this equation, you apply it to expand (2x - 1)(m + 4) by multiplying 2x and -1 each by m and 4, respectively, to simplify the expression.

Combining Like Terms

After expanding, you combine like terms, which are terms with the same variable raised to the same power. This step simplifies the equation by consolidating terms involving x and constants, making it easier to isolate the variable.

Solving Linear Equations

Solving for x involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. This process leads to finding the value of x that satisfies the equation.

Recommended video: