4.11 Two-step inequalities
Solve:
3 x - 9 > 9
2 x - 12 \leq 8
8 x + 3 \leq 6
5 y - 4 < 2
2 - x \leq - 6
6 x - 54 \geq 30
21 + 7 x \geq 21
64 \gt 8 x + 24
3 x + 27 \gt 3
8 - x \lt 6
- 9 - x \gt 4
4 \leq 1 - x
Solve:
\dfrac{- x}{- 2} \gt 6
\dfrac{x}{2} - 1 \leq 7
- 3 \leq 1 + \dfrac{x}{6}
\dfrac{x + 2}{3} \geq 2
5 > \dfrac{x - 9}{2}
\dfrac{x + 5}{- 4} > 4
7 - \dfrac{1}{7} x \gt 9
\dfrac{x}{5} + 3 > 3
Consider the inequality 21 + 7 x \gt 21:
Solve the inequality.
State whether the following values of x satisfy the inequality:
x = 0
x = 1
x = 14
x = 7
Consider the inequality 6 \left(x + 2\right) \leq 48:
Solve the inequality.
State whether the following values of x satisfy the inequality:
x = - 6
x = 6
x = 0
x = 12
Isabelle tried to solve the following inequality but made a mistake in her work.
\begin{alignedat}{4} \text{Step 0 :} \enspace & \dfrac{x}{4} & + 2 & &\, \lt & -3 \\ \text{Step 1 :} \enspace & & \dfrac{x}{4} & &\, \lt & -1 \\ \text{Step 2 :} \enspace & & x & &\, \lt & -4 \end{alignedat}
Determine which step is incorrect and explain the error.
Norton tried to solve the following inequality but made a mistake in his work.
\begin{alignedat}{4} \text{Step 0 :} \enspace & -4x & - 2 & & \, \geq & \, 18 \\ \text{Step 1 :} \enspace & & -4x & & \, \geq & \, 20 \\ \text{Step 2 :} \enspace & & x & & \, \geq & -5 \end{alignedat}
Determine which step is incorrect and explain the error.
State whether the following statements are equivalent to 3 - x \geq -5:
- x \leq -8
x + 3 \leq 5
x - 5 \leq 3
8 \geq x
-x - 5 \geq -3
x \leq -8
5 + x \leq 3
-x \geq -8
For each of the following:
Solve the inequality.
Graph the solution to the inequality on a number line.
2 x - 2 \lt 6
3 \lt 4 x - 1
- 4 x + 9 \gt 9
- 7 x - 5 \leq 2
20 - 12 x \lt 32
4 x - 4 \geq 8
3 x + 1 > 4
6 x + 27 \leq 0
2 \leq 3 x - 1
7 < 4 x + 3
3 > 5 x + 8
- 4 x + 1 \geq 9
- 3 x - 5 \geq 4
7 - x > 13
\dfrac{x - 7}{6} \gt - 1
1 \leq \dfrac{x - 5}{3}
\dfrac{x - 2}{8} \leq - 1
2 - \dfrac{x}{3} \geq 0
\dfrac{x}{2} + 4 > 1
\dfrac{x}{6} - 1 \leq 1
Tyesha tried to graph the solution to the inequality -2 \left( x - 3 \right) \lt 6 on a number line. However, her answer is incorrect:
Determine the error(s) and explain how to fix them.
Percy tried to graph the solution to the inequality 4x + 28 \geq -8 on a number line. However, his answer is incorrect.
Determine the error(s) and explain how to fix them.