Use a graphing calculator to solve each linear equation. 7x-2x+ 4-5=3x+1

Verified step by step guidance

1. First, simplify both sides of the equation by combining like terms. On the left side, combine the terms involving \( x \) and the constant terms separately: \( 7x - 2x + 4 - 5 \).
2. Rewrite the simplified equation so that it looks like \( \text{(simplified left side)} = 3x + 1 \).
3. Next, use the graphing calculator to graph the two expressions as separate functions: \( y = \text{(simplified left side)} \) and \( y = 3x + 1 \).
4. Find the point(s) where the two graphs intersect. The \( x \)-coordinate(s) of the intersection point(s) represent the solution(s) to the equation.
5. Verify the solution by substituting the \( x \)-value(s) back into the original equation to ensure both sides are equal.

Key Concepts

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, in 7x - 2x, both terms contain x, so they can be combined to 5x. This step simplifies the equation and makes it easier to solve.

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. The goal is to simplify the equation to the form x = a number.

Using a Graphing Calculator

A graphing calculator can solve equations by graphing both sides as functions and finding their intersection point. This visual method helps identify the solution where the two expressions are equal. It is especially useful for checking work or solving more complex equations quickly.