MATH 7.10A/B-CW#1-EQUATIONS AND INEQUALITIES

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What is an equation?

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An equation is a mathematical statement that asserts the equality of two expressions, typically written in the form 'A = B'. For example, 2x + 3 = 7 is an equation.

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. For example, x + 5 > 10 is an inequality.

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What does it mean to solve an equation?

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To solve an equation means to find the value(s) of the variable(s) that make the equation true. For example, solving 2x + 3 = 7 gives x = 2.

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What is the difference between an equation and an inequality?

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An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

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What is a variable in mathematics?

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A variable is a symbol, often a letter, that represents an unknown value in an equation or inequality. For example, in the equation x + 2 = 5, x is the variable.

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What does it mean to isolate a variable?

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To isolate a variable means to manipulate an equation or inequality so that the variable is on one side and all other terms are on the other side. For example, in 2x + 3 = 7, isolating x gives x = 2.

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What is the solution set of an equation?

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The solution set of an equation is the set of all values that satisfy the equation. For example, the solution set of x + 2 = 5 is {3}.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). For example, in the equation y = 2x + 1, the slope is 2.

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution set. For example, 2x + 3 = 7 and x = 2 are equivalent equations.