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What is the answer to an inequality called?

A “solution” of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.

Why do you flip signs for inequalities?

When you multiply both sides by a negative value you make the side that is greater have a “bigger” negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Does the inequality sign change when subtracting?

Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.

Does the inequality sign change when taking square root?

Taking a square root will not change the inequality (but only when both a and b are greater than or equal to zero).

Does squaring an inequality flip the sign?

The function y = x2 is increasing for x ≥ 0. (Figure 1) Hence squaring both sides of an inequality will be valid as long as both sides are non-negative. For example, the function y = x2 is decreasing for x < 0. Hence, squaring inequalities involving negative numbers will reverse the inequality.

What happens when you invert an inequality?

Multiplying or dividing the same negative number to both sides of an inequality reverses the inequality – this is also called the flip rule of inequalities. Let us now try and understand these two rules for inequalities using the examples below.

What is the use of quadratic inequalities?

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2×2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation.

When she adds 2 to both sides the equation 4x 3x results which is the best interpretation of this equation?

which is the best interpretation of this equation? the equation has infinite solutions.

Which is the solution set of the compound inequality?

When the two inequalities are joined by the word or, the solution of the compound inequality occurs when either of the inequalities is true. The solution is the combination, or union, of the two individual solutions.

Which are correct representations of the inequality 6x ≥ 3/4 2x 1 )? Select three options quizlet?

  • Answer: Option A, B and C are the correct options.
  • Step-by-step explanation: Inequality has been given as 6x ≥ 3 + 4(2x – 1)
  • 6x ≥ 3 + 8x – 4 [Option B is the correct option] 6x ≥ 8x – 1.
  • 1 ≥ 2x [Option A is the correct option] x ≤
  • Option C represents the inequality drawn on the number line.

How do you add two inequalities?

First of all, we can add inequalities with the same direction. In other words, with the inequalities pointing in the same direction. So if a is greater than b and c is greater than d, then we can just add them together. A + c has to be greater than b + d.

Can we multiply two inequalities?

Multiplying or dividing the same positive number to both sides of an inequality does not change the inequality. As you can see from the above example, adding, subtracting, multiplying, or dividing both sides of an inequality with the same positive number does not change the inequality.

Does multiplying by a negative change the inequality?

Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa.

What is the first step in graphing a linear inequality in two variables?

A linear inequality occurs when the equal sign in a linear equation is replaced with an inequality symbol. To graph a linear inequality in two variables, first graph the line as if it were a linear equation. Identify whether the inequality includes the “or equal to” aspect.