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

Verified step by step guidance

1. Start by expanding the left side of the equation: distribute -4 across the terms inside the parentheses in \(-4(2x - 6)\), which gives \(-4 \times 2x\) and \(-4 \times (-6)\).
2. Rewrite the equation after distribution: \(-8x + 24 + 8x = 5x + 24 + x\).
3. Combine like terms on both sides: on the left side, combine \(-8x\) and \$8x\(; on the right side, combine \)5x\( and \)x$.
4. Simplify the equation to isolate the variable terms on one side and constants on the other side.
5. Solve for \(x\) by dividing or multiplying as needed to get \(x\) alone.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term outside the parentheses by each term inside the parentheses. For example, -4(2x - 6) becomes -8x + 24. This step simplifies expressions and is essential before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, 8x and 5x can be combined to 13x. This process simplifies equations and makes it easier to isolate the variable.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating the variable on one side by performing inverse operations such as addition, subtraction, multiplication, or division. The goal is to simplify the equation to the form x = number.