compare and contrast the ways in which solving a linear inequality is similar / dissimilar to solving a linear equation please explain
The procedure is the same except the
inequality sign is reversed when multiplying or dividing by a negative
number.
Please please i need help with solving this linear inequality x6+1/8=x2-3/4 don't know what I'm doing thanks
Solving a linear inequality is quite similar to solving a linear equation, but there are a few notable differences. Let's first examine how the processes are similar:
Similarities:
1. Both involve operations on both sides of the equation or inequality.
2. Addition, subtraction, multiplication, and division can be used to manipulate both equations and inequalities.
3. The goal is to isolate the variable on one side of the equation or inequality.
Now let's explore the differences between solving a linear inequality and solving a linear equation:
Differences:
1. In an equation, the goal is to find the value or values of the variable that make the equation true. In contrast, when solving an inequality, we are determining the range of values of the variable that satisfy the inequality.
2. When solving an inequality, if you multiply or divide both sides by a negative number, the direction of the inequality sign must be reversed. This is because multiplying or dividing by a negative number switches the inequality's direction.
3. For an equation, there can be only one solution that satisfies the equation. However, when solving an inequality, there can be an infinite number of solutions that satisfy the given inequality. Therefore, the solution to an inequality is typically expressed using interval notation or graphically on a number line.
To summarize, while the basic principles of manipulating equations and inequalities are similar, the primary difference lies in determining the range of values that satisfy the inequality versus finding the specific solution(s) that satisfy an equation.