Taking Sides

Learning Focus

Compare expressions and solve inequalities by finding where two sides are equal and deciding which is larger.

Big idea

To compare $A(x)$ and $B(x)$:

1. Solve $A(x)=B(x)$ to find the boundary value.
2. Test a value on each side (or solve algebraically) to see where $A>B$ or $A<B$.

Solving an inequality is the same as asking "for which $x$ is one side bigger?" Remember to flip the sign when dividing by a negative.

Worked example

Compare $3x+4$ and $2x+10$.

• Equal: $3x+4=2x+10\Rightarrow x=6$
• $3x+4>2x+10\Rightarrow x>6$
• $3x+4<2x+10\Rightarrow x<6$

Test $x=0$: $4<10$ ✓. Test $x=10$: $34>30$ ✓.

Takeaways

• Equal expressions give the boundary.
• Test values on each side of the boundary.
• Flip the inequality sign when multiplying/dividing by a negative.