Solve each equation. -4(2x-6) +8x= 5x+24+x

Verified step by step guidance

1. Distribute the -4 into the terms inside the parentheses: $-4(2x-6)$ becomes $-8x+24$.
2. Rewrite the equation with the distributed terms: $-8x+24+8x=5x+24+x$.
3. Combine like terms on both sides of the equation. On the left side, $-8x+8x$ simplifies to 0, so you have $24=5x+24+x$.
4. Combine like terms on the right side: $5x+x$ becomes $6x$, so the equation is $24=6x+24$.
5. Subtract 24 from both sides to isolate the term with $x$: $24-24=6x+24-24$, which simplifies to $0=6x$.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term inside a set of parentheses. In the given equation, applying the distributive property to -4(2x - 6) is essential to simplify the expression before solving for x.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. In the equation, after applying the distributive property, it is crucial to combine the x terms and constant terms on both sides to isolate the variable and solve for x.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, or division. Understanding this concept is vital for determining the solution to the equation presented.