3.04 Interval notation
Write the interval notation for each of the following pictured inequalities:
For each of the following inequalities express the solutions of the inequality using interval notation:
x < - 7
x \leq 6
x \geq - 4
- 7 \leq x \leq 3
For each of the following pictured inequalities:
Write the interval notation.
Express this interval as an inequality of x.
Consider the inequality 5 x - 8 \leq 4 \left(x - 2\right).
Solve the inequality.
Express the solutions to the inequality using interval notation.
Express the solutions of the following compound inequalities using interval notation:
x > 2 or x > 6
x > 3 and x > 5
For each of the following inequalities:
Express the solutions of the inequality using interval notation.
Graph the interval on a number line.
x \leq 3
x < 8
x > \dfrac{5}{2}
x < 2 \text{ or } x < - 5
x \leq - 5 \text{ or } x \geq 2
Consider the set described by the inequalities 4 x - 10 < -2 or 4 x - 10 > 2:
Solve the first inequality, 4 x - 10 < - 2, for x.
Solve the second inequality, 4 x - 10 > 2, for x.
Write the solution set for x in interval notation.
Graph the solution set for x in a number line.
Consider the compound inequality 8 x \leq 9 x - 3 \leq 27 - x:
Solve the left hand inequality, 8 x \leq 9 x - 3, for x.
Solve the right hand inequality, 9 x - 3 \leq 27 - x, for x.
Write the solution set for x.
Consider the compound inequality x + 2 < 0 \text{ or } 6 x > 30:
Simplify the compound inequality.
Express the solutions of the inequality using interval notation.
Graph the interval on a number line.
Consider the compound inequality - 2 \leq 1 - 2 x < 2:
Solve the compound inequality.
Write the solution set for x in interval notation.
Graph the solution set for x in a number line.