Math 1 Equations and Inequalities

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What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'. For example, x + 4 < -3x + 12 < 24 is a compound inequality.

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How do you solve a compound inequality?

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To solve a compound inequality, isolate the variable in the middle inequality and ensure the solution satisfies all parts of the compound inequality.

Front

What is the solution set of the compound inequality x + 4 < -3x + 12 < 24?

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The solution set is -4 < x < 2.

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Back

The first step is to find a common denominator to eliminate the fractions.

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Back

The solution is k = -12.

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What does it mean if an equation has no solution?

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An equation has no solution if there are no values for the variable that make the equation true.

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What is the solution to the equation 2(3x + 4) = 3(2x + 1)?

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The solution is no solution.

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What is an even integer?

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An even integer is any integer that is divisible by 2, such as -4, -2, 0, 2, 4.

Front

If the sum of three consecutive even integers is 54, how can you express them?

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Let the integers be x, x+2, and x+4. Then, x + (x + 2) + (x + 4) = 54.

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What is the sum of the smallest and largest integers if the sum of three consecutive even integers is 54?

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The sum of the smallest and largest integers is 36.