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 with \(x\) and the constant terms separately: \(7x - 2x + 4 - 5\).
2. Rewrite the simplified equation so it looks like \(\text{(simplified left side)} = 3x + 1\).
3. Next, rearrange the equation to isolate all \(x\)-terms on one side and constants on the other side. This means subtracting or adding terms to both sides accordingly.
4. Once the equation is simplified to the form \(ax = b\), where \(a\) and \(b\) are constants, use your graphing calculator to graph the functions \(y = \text{left side expression}\) and \(y = \text{right side expression}\).
5. Find the point of intersection of the two graphs on the calculator. The \(x\)-coordinate of this point is the solution to the equation.

Key Concepts

Simplifying Linear Equations

Simplifying linear equations involves combining like terms and performing arithmetic operations to rewrite the equation in a simpler form. For example, combining 7x and -2x results in 5x, which makes it easier to isolate the variable and solve the equation.

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable (usually x) is on one side alone. This is done by adding, subtracting, multiplying, or dividing both sides of the equation to solve for the variable's value.

Using a Graphing Calculator to Solve Equations

A graphing calculator can solve linear equations by graphing both sides as functions and finding their intersection point. The x-coordinate of the intersection represents the solution to the equation, providing a visual and numerical method to verify answers.