Equations loosen into inequalities this week, with one famous trap: multiplying or dividing by a negative flips the sign. Proportions arrive alongside, two ratios set equal, opened with a cross multiplication.
What you have to be able to do
Solve and graph an inequality
Flip the inequality sign at the right moment and only then
Solve a proportion by cross multiplying
The procedures
Solving inequalities
Use the same two rules as equations.
Multiplying or dividing both sides by a negative flips the direction of the sign.
Adding or subtracting never flips anything.
Graphing them
An open circle for strict: less than, greater than.
A closed circle when equals is included.
Shade toward every number that makes it true.
Proportions
A proportion says two ratios are equal.
Cross multiply: top left times bottom right equals top right times bottom left.
Then divide to finish, like any equation.
Worked
WORKED
Solve −3x < 12. Divide both sides by −3. Dividing by a negative flips the sign. ANSWER: x > −4
WORKED
Solve x4 = 96. Cross multiply: 6x = 36. Divide by 6. ANSWER: x = 6
Terms
Term
Meaning
inequality
a statement using less than or greater than
proportion
two ratios set equal to each other
ratio
a comparison of two quantities by division
Check yourself
1. Solve: x + 5 > 9
2. Solve: −2x ≥ 10
3. Solve: 35 = x20
reveal answers
x > 4 · x ≤ −5 · x = 12
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 10, inequalities and proportionsalgebra 1 · oda