Explain how solving a linear inequality is similar to solving a linear equation.

Explain how solving a linear is different from solving a linear equation.

Do the equations x = 5y + 3 and x = 5y – 3 have the same solution? How might you explain your answer to someone who has not learned algebra?

Solving a linear inequality is similar to solving a linear equation in several ways. Both involve finding the value or values of the variable that make the statement true. Additionally, the methods used to solve linear inequalities often resemble the steps taken to solve linear equations. However, there are also some important differences to consider.

When solving a linear equation, the goal is to determine the specific value of the variable that satisfies the equation. The aim is to isolate the variable on one side of the equation by performing the same operations on both sides. These operations may include addition, subtraction, multiplication, or division, usually with the goal of canceling out certain terms or coefficients.

On the other hand, when solving a linear inequality, the objective is to find all the values of the variable that make the inequality true. This includes an entire range of solutions, rather than a single solution as in the case of a linear equation. In order to find this range, similar operations are performed on both sides of the inequality. However, there is one crucial difference: when multiplying or dividing both sides of the inequality by a negative number, the direction of the inequality symbol must be reversed.

To summarize, solving a linear inequality shares some similarities with solving a linear equation, such as using similar operations to isolate the variable. However, solving a linear inequality also involves finding a range of solutions and requires paying attention to the direction of the inequality when applying certain operations.