Algebra Inequalities Quiz 5.1-5.3

Solving Inequalities

• 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.