Linear Inequalities Flashcards

All 4 cards in this deck

What are the steps to solve a linear inequality with brackets and unknowns on both sides?
e.g. $5(x-3) > 2(x+3)$

1. Expand both sides: $5x - 15 > 2x + 6$
2. Collect the unknowns on one side: $3x > 21$
3. Divide by the coefficient: $x > 7$

What must you do to an inequality sign when you multiply or divide both sides by a negative number?
e.g. $-2x < 6$

Reverse it.
$-2x < 6$ gives $x > -3$

What are the steps to form and solve an inequality from a context?
e.g. a rectangle with sides $x$ cm and $(x+2)$ cm has perimeter less than $20$ cm

1. Form the inequality: $4x + 4 < 20$
2. Solve it: $x < 4$
3. Add any restriction from the context: lengths are positive, so $0 < x < 4$

True or false? The solution $x \geqslant 5$ includes the value $5$ itself.

True.
$\geqslant$ means "greater than or equal to", so the boundary value is included.