Math Tests - mathematics practice questions

Variable inequalities with adding/subtracting

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Inequalities

To solve the inequality we need to isolate the variable (a letter used as a placeholder for an unknown value, mostly x or y) to one side and everything else to the other side. All inequalities have two sides: a left side (LS) and a right side (RS). The relationship between sides can be < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).

We can to do the same thing (adding, subtracting, multiplying every term, dividing every term) to both sides, what can help to bring like terms (numbers) together to one side and isolate the variable on the other side.

Example:
$$8−x < 3x$$
$$8 < 3x + x$$
$$8 < 4x$$
$$8÷4 < x$$
$$2 < x$$


Variable inequalities with multipl./division

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Inequalities

To solve the inequality we need to isolate the variable (a letter used as a placeholder for an unknown value, mostly x or y) to one side and everything else to the other side. All inequalities have two sides: a left side (LS) and a right side (RS). The relationship between sides can be < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).

We can to do the same thing (adding, subtracting, multiplying every term, dividing every term) to both sides, what can help to bring like terms (numbers) together to one side and isolate the variable on the other side.

Example:
$$8−x < 3x$$
$$8 < 3x + x$$
$$8 < 4x$$
$$8÷4 < x$$
$$2 < x$$


Choose the correct inequality that best describes each graph

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Choose the correct interval that best describes graph

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Interval notation

Interval notation is a method of writing down a set/range of numbers. We need brackets and a pair of numbers representing two endpoints of a number range. We use for this brackets [] and parentheses () for this. Brackets [ ] mean that the endpoint of the range is included (this is drawn on a number line with a full dot). Parentheses () mean that the endpoint is excluded and doesn't contain the listed element (this is drawn on a number line with empty dot). So for [0, 10), the range starts with 0 (and includes it), but ends just before 10 (excluding 10).

Infinity symbols ∞ and −∞ are always accompanied by round brackets (). For example, [2, ∞) is the interval of real numbers greater or equal to 2.



   
   

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