Questions and Answers
Solve the inequality: r - (-5) > -7.
r > -2
Solve the inequality: 3x + 8 ≤ 4x.
x ≥ 8
Solve the inequality: n - 2.5 ≥ -5.
n ≥ -2.5
Solve the inequality: -13h ≤ 52.
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Solve the inequality: 39 > 13p.
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Solve the inequality: 0.1x ≥ -4.
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Solve the inequality: 4u - 6 ≥ 6u - 20.
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Solve the inequality: 3(z + 1) + 11 < -2(z + 13).
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Solve the inequality: 5n - 3(n - 6) ≥ 0.
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Solve the inequality: 3r + 2(4r + 2) ≤ 2(6r + 1).
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Study Notes
Solving Inequalities
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Inequality Notation: In inequalities, symbols such as
<,>,≤, and≥indicate the relationship between two expressions.
Card 1: Inequality with r
- From r - (-5) > -7, simplifying yields r + 5 > -7, which leads to r > -12.
Card 2: Inequality with x
- Starting with 3x + 8 ≤ 4x, rearranging gives 8 ≤ x, resulting in x ≥ 8.
Card 3: Inequality with n
- From n - 2.5 ≥ -5, adding 2.5 to both sides results in n ≥ -2.5.
Card 4: Inequality with h
- The inequality -13h ≤ 52 when divided by -13 gives h ≥ -4 (note that inequality direction reverses when dividing by a negative).
Card 5: Inequality relating p
- Given 39 > 13p, moving variables leads to p < 3 after dividing by 13.
Card 6: Inequality with x
- Starting with 0.1x ≥ -4, multiplying through by 10 yields x ≥ -40.
Card 7: Inequality with u
- From 4u - 6 ≥ 6u - 20, simplifying results in u ≤ 7 after collecting like terms.
Card 8: Complex Inequality with z
- The expression 3(z + 1) + 11 < -2(z + 13) simplifies to yield z < -10 after distributing and combining like terms.
Card 9: Inequality with n
- Starting with 5n - 3(n - 6) ≥ 0, simplifying leads to n ≥ -9 after distributing and combining terms.
Card 10: Inequality with r
- The equation 3r + 2(4r + 2) ≤ 2(6r + 1) simplifies to r ≥ 2 after rearranging and collecting like terms.
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Description
Test your knowledge of algebra and inequalities with this quiz covering sections 5.1 to 5.3. You'll solve various inequalities and hone your skills in manipulating and understanding them. Perfect for students looking to solidify their understanding of the concepts.
