Inequalities

Inequality symbols, showing inequalities on a number line, and solving linear inequalities including reversing the sign when multiplying or dividing by a negative.

Symbols and number lines

$x > 3$ means $x$ is greater than $3$; $x \ge 3$ means greater than or equal to $3$. On a number line, an open circle means the end value is not included ($>$, $<$) and a closed circle means it is included ($\ge$, $\le$).

Solving

Solve an inequality like an equation, with one extra rule.

Example 1●

Solve $3x - 4 \le 11$.

$3x \le 15$, so $x \le 5$

Example 2●●

Solve $5 - 2x > 13$.

$-2x > 8$

$x < -4$

Divide by −2 and flip

Flashcards

Open circle

$<$ or $>$ (not included)

Closed circle

$\le$ or $\ge$ (included)

When does the sign flip?

Multiplying or dividing by a negative.

Practice

Solve $3x - 4 \le 11$.
Solve $5 - 2x > 13$.
Which uses a closed circle on a number line?
Solve $\dfrac{x}{2} + 1 < 4$.
Solve $-3x \le 12$.
What is the smallest whole number that satisfies $2x + 1 > 8$?
Is $x = -1$ a solution of $4 - x > 3$?
Solve $2(x - 3) \ge x + 1$.