ACT Preparation / Unit 9 ACT 0822 worked example, 60 to 90 seconds
Solving a Linear Inequality
The idea
To solve a linear inequality, work in four steps. First, distribute and combine like terms on each side. Second, gather the variable on one side and the numbers on the other. Third, divide by the coefficient, reversing the sign if the coefficient is negative. Fourth, test one value inside the solution and one outside.
In practice
Worked example: 5 − 2(x + 4) ≥ 3x + 7. Step one: 5 − 2x − 8 ≥ 3x + 7, so −2x − 3 ≥ 3x + 7. Step two: −5x ≥ 10. Step three: dividing by −5 reverses the sign: x ≤ −2. Step four: x = −3 gives 3 ≥ −2, true; x = 0 gives −3 ≥ 7, false.
Where people slip
Gathering the variable on the side where its coefficient stays positive avoids the flip altogether: −3 − 7 ≥ 5x gives −2 ≥ x, the same answer.
Your place on the trail
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