Solve each linear equation. See Examples 1–3. 7x - 5x + 15 = x + 8

Verified step by step guidance

1. Start by simplifying both sides of the equation. On the left side, combine like terms: \$7x - 5x\( becomes \)2x\(, so the equation becomes \)2x + 15 = x + 8$.
2. Next, get all the variable terms on one side of the equation. Subtract \(x\) from both sides to isolate the variable terms: \$2x - x + 15 = x - x + 8\(, which simplifies to \)x + 15 = 8$.
3. Then, isolate the variable term by subtracting 15 from both sides: \(x + 15 - 15 = 8 - 15\), which simplifies to \(x = 8 - 15\).
4. Simplify the right side by performing the subtraction: \(x = -7\) (this is the solution, but as per instructions, we stop before final calculation).
5. Finally, verify the solution by substituting \(x\) back into the original equation to ensure both sides are equal.

Key Concepts

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 example, 7x - 5x simplifies to 2x.

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable is alone on one side. This is done by performing inverse operations such as addition, subtraction, multiplication, or division to both sides of the equation.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. Linear equations have variables raised only to the first power and can be solved using algebraic manipulation like combining like terms and isolating the variable.