Solving Inequalities

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

The symbol '≤' means 'less than or equal to'. It indicates that one value is either less than or equal to another value.

The symbol '≥' means 'greater than or equal to'. It indicates that one value is either greater than or equal to another value.

To solve, first isolate x: $$-4x ≤ 54 - 14$$ , which simplifies to $$-4x ≤ 40$$ . Dividing by -4 (and flipping the inequality) gives $$x ≥ -10$$ .

Distributing gives $$-10x - 10 + 5x > 15$$ . Combining like terms results in $$-5x - 10 > 15$$ . Adding 10 gives $$-5x > 25$$ , and dividing by -5 (flipping the inequality) gives $$x < -5$$ .

Adding 4 gives $$6x < 18$$ . Dividing by 6 results in $$x < 3$$ .

Subtracting 9 gives $$s ≥ -34$$ .

The inequality is $$y - 5 > 13$$ .

The first step is to isolate the variable on one side of the inequality.

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.