Solving Equations/Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

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What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side.

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What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

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What does 'x > 5' mean on a number line?

Back

It means that x can take any value greater than 5, represented by an open circle at 5 and a line extending to the right.

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What does 'x ≤ 3' mean on a number line?

Back

It means that x can take any value less than or equal to 3, represented by a closed circle at 3 and a line extending to the left.

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What is the first step in solving the equation 5x + 34 = -2(-7x + 1)?

Back

The first step is to simplify the right side of the equation: -2(-7x + 1) becomes 14x - 2.

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What does it mean if an equation has infinitely many solutions?

Back

It means that there are countless values for the variable that satisfy the equation, often occurring when both sides of the equation are identical.

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How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.