Question

compound inequalities (l1)
this is the only question in this section.
question
solve for x and graph the solution on the number line below.
2x - 1 ≤ 19 or 23 < 2x - 1
answer
inequality notation
number line

Explanation:

Step1: Solve the first inequality

Solve $2x - 1\leq19$. Add 1 to both sides: $2x-1 + 1\leq19 + 1$, which simplifies to $2x\leq20$. Then divide both sides by 2: $\frac{2x}{2}\leq\frac{20}{2}$, so $x\leq10$.

Step2: Solve the second inequality

Solve $23<2x - 1$. Add 1 to both sides: $23 + 1<2x-1 + 1$, which simplifies to $24<2x$. Then divide both sides by 2: $\frac{24}{2}<\frac{2x}{2}$, so $12

Step3: Combine the solutions

The compound - inequality is an "or" statement. The solution in inequality notation is $x\leq10$ or $x > 12$.

Answer:

Inequality Notation: $x\leq10$ or $x>12$
For the number - line:

• For $x\leq10$, draw a closed circle at 10 and an arrow pointing to the left.
• For $x > 12$, draw an open circle at 12 and an arrow pointing to the right.