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Can linear equations and linear inequalities be solved the same way?
Wiki User
∙ 13y ago
Yes, but with the following two rules to remember. If you multiply or divide both sides by a negative number, then the inequality sign is reversed (> becomes <, or < becomes >). Adding and subtracting numbers have no effect on the direction of the inequality. Also, if you have a 'not equals' sign, then it is unaffected by the multiplication.
The same is true if you take the reciprocal of both sides.
Example: with the equation: 1/x = 2, take the reciprocal and x = 1/2. With the inequality 1/x < 2, this becomes x > 1/2. You could also solve it by multiplying both sides by x, then dividing both sides by 2, and get 2 < x, which is the same as x > 2.
Another example: 3 - x > 7. Subtract 3 from both sides: -x > 4. Multiply both sides by -1: x < -4.
You could also go about this as: add x to both sides: 3 > 7 + x, then subtract 7 from both sides: -4 > x, which means the same as x < -4
Wiki User
∙ 13y ago
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Why can linear equations and linear inequalities be solved the same way?
Somewhat, but the rules are a bit different for inequalities. Example. -2X > 4 X < - 2 See, sign changes when dividing by negative coefficient.
How do you solve algebra inequalities?
Algebraic inequalities can be solved in the same fashion as algebraic equations. The goal here, as in algebraic equations, is to isolate the variable. The one thing to remember, however, is that when dividing or multiplying both sides by a negative number, one must switch the inequality sign.
Are the methods for solving linear and compound inequalities the same?
Yes
What are linear equations with the same solutions called?
They are called simultaneous equations.
Can a linear equation and a linear Equality be solved the same way?
Yes.
Why can linear equations and linear inequalities be solved the same way?
Somewhat, but the rules are a bit different for inequalities. Example. -2X > 4 X < - 2 See, sign changes when dividing by negative coefficient.
How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
What consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
How do you solve algebra inequalities?
Algebraic inequalities can be solved in the same fashion as algebraic equations. The goal here, as in algebraic equations, is to isolate the variable. The one thing to remember, however, is that when dividing or multiplying both sides by a negative number, one must switch the inequality sign.
Compare and contrast equations and inequalities?
Inequalities and equations are both the same because they are both mathematical expression and they both use the same steps EXCEPT for the end. Inequalities and equations are both different because equations have an equal sign, the answer is not an interval, and the answer is a specific answer. Not a range. While inequalities don't have an equal sign, its answer is an interval, and it's answer is in a range.
How are the rules for solving inequalities similar to those for solving equations?
Solving inequalities and equations are the same because both have variables in the equation.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
Can linear equations and linear inequality be solved the same way?
Basically. If the inequality's sign is < or ≤, then you shade the part under the line. If the inequality's sign is > or ≥, then you shade the part over the line.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
Are the methods for solving linear and compound inequalities the same?
Yes
What are two or more linear equations using the same variables called?
A system of linear equations.
Why are linear equation and linear inequalities not solved in the same manner?
Although there are similarities, the solutions to a linear equation comprise all points on one line: a one-dimensional object. The solutions to a linear inequality comprise all points on one side [or the other] of a line: a two-dimensional object.
