Absolute Value Problems Worksheet

Are you a math teacher searching for a concise and effective way to help your students practice solving absolute value problems? Look no further, as we have created an entity-specific worksheet designed to enhance their understanding of this crucial concept. This worksheet provides a variety of carefully crafted problems that focus on the subject of absolute value, offering students the practice they need to reinforce their skills and develop confidence in their problem-solving abilities.

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What are the absolute values of -5, 7, and 0?

The absolute values of -5, 7, and 0 are 5, 7, and 0 respectively. The absolute value of a number is its distance from zero on the number line, regardless of its sign.

Solve the equation |2x - 3| = 5.

To solve the equation |2x - 3| = 5, we first set up the two possible scenarios when the absolute value is positive or negative. For when 2x - 3 is positive, we have 2x - 3 = 5, which simplifies to 2x = 8 and x = 4. For when 2x - 3 is negative, we have -(2x - 3) = 5, which simplifies to -2x + 3 = 5 and then -2x = 2, giving x = -1. Therefore, the solutions to the equation are x = 4 and x = -1.

Find the distance between -4 and 9 on a number line.

The distance between -4 and 9 on a number line is 13 units.

If |a| = 8, what are the possible values of a?

The possible values of a are 8 and -8, as the absolute value of a means the distance of a from zero on the number line, which can be either positive or negative.

Solve the inequality |3x - 2| < 4.

To solve the inequality |3x - 2| < 4, we need to consider two cases: when 3x - 2 is positive and when it is negative. For the case where 3x - 2 is positive, we have 3x - 2 < 4 which simplifies to x < 2. For the case where 3x - 2 is negative, we have -(3x - 2) < 4 which simplifies to x > -2/3. Combining the results, the solution to the inequality is -2/3 < x < 2.

Is the absolute value of a negative number positive, negative, or zero?

The absolute value of a negative number is always positive.

Find the solution set for |x + 2| ≥ 10.

The solution set for |x + 2| ≥ 10 is x ≤ -12 or x ≥ 8.

If |b| = |c|, what can you conclude about the values of b and c?

If |b| = |c|, it means that the absolute values of b and c are equal. This implies that either both b and c are positive or both are negative. In other words, b and c have the same magnitude but could have different signs.

Solve the inequality |4x + 3| > 7.

To solve the inequality |4x + 3| > 7, we first set up the two cases: 4x + 3 > 7 and 4x + 3 < -7. Solving the first case gives us x > 1 and solving the second gives us x < -5/4. Therefore, the solution to the inequality is x < -5/4 or x > 1.

Find the coordinates of the point (x, y) on a graph if |x| + |y| = 5.

The coordinates of the points (x, y) on the graph where |x| + |y| = 5 can be found by considering all possible combinations of x and y that satisfy this equation. These points form a square with vertices at (5, 0), (-5, 0), (0, 5), and (0, -5).