Solve the given equation or inequality graphically. a. -2 x+3=3 x-7 b. -2 x+3 ≤3 x-7

Name: Problem 24, Chapter 2: College Algebra
Uploaded: 2020-07-23T18:51:28-08:00
Duration: 2 min 50 s
Channel: Ankit Gupta
Description: Solve the given equation or inequality graphically. a. -2 x+3=3 x-7 b. -2 x+3 ≤3 x-7

step 1 The equation given in this problem is minus 2x plus 3 is equal to 3x minus 7. And we also have a

Solve the given equation or inequality graphically. a. -2...

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. In the context of the problem, the solution involves balancing the equation so that the expressions on either side are equal. This method provides the x-value at which two expressions yield the same result.

Graphical Representation of Linear Equations

Graphing a linear equation involves plotting a straight line on the coordinate plane using its slope and y-intercept. When solving the equation graphically, each expression is graphed as a line, and their intersection point represents the solution where the two expressions are equal.

Linear Inequalities

A linear inequality is similar to a linear equation but uses inequality symbols (such as ?, ?, <, or >) to define a range of values that satisfy the condition. The solution set of a linear inequality is usually a range of values rather than a single number.

Graphical Solution of Inequalities

Solving an inequality graphically involves plotting the boundary line obtained from the associated equation and then determining which side of the line satisfies the inequality. If the inequality is inclusive (using ? or ?), the boundary line is drawn as a solid line; otherwise, for strict inequalities (< or >), it is drawn as a dashed line. The region of the graph that meets the inequality condition is then shaded to represent the solution set.

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