Solve each equation. 3x+5 - 5(x+1)= 6x+7

Verified step by step guidance

1. Start by expanding the expression on the left side of the equation: distribute the -5 across the terms inside the parentheses in \$3x + 5 - 5(x + 1) = 6x + 7\(. This means rewriting it as \)3x + 5 - 5x - 5$.
2. Combine like terms on the left side: group the \(x\) terms together and the constant terms together. This simplifies the left side to \((3x - 5x) + (5 - 5)\).
3. Simplify the combined terms: calculate \$3x - 5x\( and \)5 - 5$ to get the simplified left side expression.
4. Set the simplified left side equal to the right side of the equation, which is \$6x + 7$, and write the new equation.
5. Isolate the variable \(x\) by moving all \(x\) terms to one side and constants to the other side. Then solve for \(x\) by dividing both sides by the coefficient of \(x\).

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 5(x + 1) by distributing the 5 to both x and 1.

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 by reducing the number of terms.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This typically involves isolating the variable on one side by performing inverse operations such as addition, subtraction, multiplication, or division.