Multi-step inequalities: solve, graph and write from a story

Answer Key - Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari gets 2x + 11 ≥ 5x - 4 on a puzzle card. What inequality gets x by itself?

   x ≤ 5
2. 2.

   Bo gets 3x - 2 < 7x + 10 on a puzzle card. What inequality gets x by itself?

   x > -3
3. 3.

   Esme gets 6x + 5 > 2x - 11 on a puzzle card. What inequality gets x by itself?

   x > -4
4. 4.

   Kira's challenge card says -2(x - 3) > 10. What inequality gets x by itself?

   x < -2
5. 5.

   Milo's challenge card says 4 - 5x ≥ 19. What inequality gets x by itself?

   x ≤ -3
6. 6.

   Pia spreads the bracket in 3(x - 2) ≤ x + 8 first. What inequality gets x by itself?

   x ≤ 7
7. 7.

   Tala spreads the bracket in 4(x - 1) ≥ 2x + 6 first. What inequality gets x by itself?

   x ≥ 5
8. 8.

   Zee's bean plant is 4 cm, growing 3 cm a week; the pea plant is 16 cm, growing 1 cm. What inequality shows the weeks w when the bean plant is taller?

   3w + 4 > w + 16
9. 9.

   Red kite: 10 m, climbing 2 m a minute. Blue kite: 4 m, climbing 4 m a minute. For which minutes x is Bo's red kite at most as high? What inequality shows this?

   2x + 10 ≤ 4x + 4
10. 10.

    Esme's sunny snowbank is 40 cm, losing 3 cm a day; the shady one is 26 cm, losing 1 cm. What inequality shows the days d when the sunny bank is less deep?

    -3d + 40 < -d + 26