what is the difference between solving inequalities and equations as it relates to the solution?
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The difference between solving an equation and solving an inequality. Solving Inequalities is very similar to solving Equations. ... If you multiply or divide one side of an equation or inequality by the same number, you have to multiply or divide the other side of the equation or inequality by the same number.
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We can solve quadratic inequalities graphically by first rewriting the inequality in standard form, with zero on one side. Graph the quadratic function and determine where it is above or below the x-axis. If the inequality involves “less than,” then determine the x-values where the function is below the x-axis.
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A quadratic equation has a solution set, which is a selection of values for its variables that make the expression true. ... A quadratic inequality is like a quadratic equation, except instead of using an equality, it uses an inequality, like or .
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A system of linear inequalities is often used to determine the maximum or minimum values of a situation with multiple constraints. For example, you might be determining how many of a product should be produced to maximize a profit.
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Solving Inequalities with No Solution or All Real Numbers. If the inequality states something untrue there is no solution. If an inequality would be true for all possible values, the answer is all real numbers.
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Graphing inequalities on either a number line or in the coordinate plane (with x and y axes) helps to visually represent several forms of inequalities: The graph of a linear inequality produces a region on the coordinate plane with a boundary line. Every point in that region is a solution of the inequality.
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Well for the substitution method you solve an equation for a particular variable and then substitute that equation into the other one and solve. With elimination you multiply an equation by a number and then add the two equations together and solve that way.
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As nouns the difference between solution and solve is that solution is a homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances while solve is (obsolete) a solution; an explanation.
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No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
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The solution(s) of a system of linear equations give points of intersection of specific lines or planes. The solution(s) of a system of linear inequalities give areas of intersection wherein any specific pair of points or lines are solutions. PROCESS-WISE there are little differences between solving systems.
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The key difference is with "or", x only needs to satisfy one of the inequalities. With "and", x needs to satisfy both.
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The set of all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that only numbers are admitted as solutions. Solving an equation symbolically means that expressions can be used for representing the solutions.
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If any number is a solution to an equation or inequality, as in x² ≥ 0, then we write ℝ in set notation (“all real numbers”) or (−∞, ∞) in interval notation. If no number is a solution, as in x² = −5, then we write ∅ in either notation.
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Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.
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1. An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other.
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['To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. ... ', 'The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.']
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An equation is two expressions that are equal to each other. Short Answer: an expression can include numbers, variables, operators, sets, matrices, and other single things that can all be evaluated to one thing. An equation is two expressions that are equal to each other.