Solve each equation. 5x-2(x+4)=3(2x+1)

Verified step by step guidance

1. Start by expanding the expressions on both sides of the equation: distribute the -2 across (x+4) and the 3 across (2x+1). This gives you: \(5x - 2 \cdot x - 2 \cdot 4 = 3 \cdot 2x + 3 \cdot 1\).
2. Simplify each term after distribution: \$5x - 2x - 8 = 6x + 3$.
3. Combine like terms on the left side: \( (5x - 2x) - 8 = 6x + 3\) which simplifies to \$3x - 8 = 6x + 3$.
4. Get all variable terms on one side and constants on the other by subtracting \$3x\( from both sides and subtracting \(3\) from both sides: \)3x - 8 - 3x - 3 = 6x + 3 - 3x - 3$.
5. Simplify both sides to isolate \(x\): \(-8 - 3 = 6x - 3x\), which becomes \(-11 = 3x\). Then solve for \(x\) by dividing both sides by 3.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, a(b + c) = ab + ac. This is essential for simplifying expressions like 5x - 2(x + 4) by distributing -2 to both x and 4.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions and makes solving equations easier. For instance, 5x - 2x simplifies to 3x.

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 using inverse operations like addition, subtraction, multiplication, or division.