May I Have More, Please?

Learning Focus

Write and solve inequalities from real contexts, and interpret solutions.

Big idea

Common phrases:

• "at least" $\Rightarrow\ge$; "at most" / "no more than" $\Rightarrow\le$
• "more than" $\Rightarrow>$; "fewer than" $\Rightarrow<$

Solve like an equation, except: multiplying or dividing by a negative flips the inequality sign.

Then interpret in context: restrict to whole numbers if you count objects.

Worked example

You have \50$. Tickets cost$$8$plus a$$10$fee:$8t+10\le50$.

• $8t\le40\Rightarrow t\le5$
• At most $5$ tickets.

Another: $5x+12\le50\Rightarrow x\le7.6$. For whole items, the greatest is $7$.

Negative: $-3x+1<10\Rightarrow-3x<9\Rightarrow x>-3$ (sign flips).

Takeaways

• Translate words to the correct symbol.
• Flip the sign when multiplying/dividing by a negative.
• Check that the answer makes sense in context (whole numbers?).