Flip the Sign, Watch the Dot

You'll learnto solve a linear inequality, including the sign flip, and read the exact answer from the range.

An inequality is a whole range of answers, and three small things decide which range: the flip when you scale by a negative, the open-or-filled dot at the boundary, and the exact value the question asks for from inside the set. Miss one and the arithmetic is clean while the answer points at the wrong half of the line.

8 STEPS · 6 QUICK CHECKS · ×/÷ by a negative flips the sign · open ≠ filled · v2

flip · then read the dot

Before you start

What you're looking at

A number line with an open dot at −3 and shading stretching left, beside two cards on the rules of solving inequalities.

The question

Which half of the number line is the answer, and does the boundary belong to it?

Watch for

An inequality is a whole range, not one value; later, multiplying by a negative flips the symbol and the shaded direction.

What the symbols mean

The open dot marks an excluded boundary (a filled dot would include it); the shading shows every value that solves the inequality.

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