CALCULATOR

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## Linear Inequalities Calculator

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INTRO

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An inequality is a math sentence that uses an inequality symbol ($<,≥,>,≤$) to tell us how two values or expressions compare to one another.

The inequality below reads $−4$ is less than $2$.

$−4<2$If we imagine the numbers on a number line, we can see that $−4$ is less than $2$ because it is farther to the left.

$−4$

$2$

If we divide (or multiply) an inequality by a negative number, we need to flip the inequality sign to make the inequality true again.

$−4$

$−1$

$≤$

$2$

$−1$

$4$

$≤$

$−2❎$$4$

$≥$

$−2✅$We can imagine dividing (or multiplying) by a negative as flipping the points on a number line. When we do this, we can see that $4$ is farther to the right than $−2$; therefore, the inequality becomes $4$ is greater than than $−2$.

$−4$

$2$

KEY STEPS

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## How to Solve Linear Inequalities

### Step 1. Move all the terms with the unknown variable to one side of the equation.

Use the same inverse operations on both sides to do this.

### Step 2. Move all the terms with known values or variables to the other side of the equation.

Use the same inverse operation on both sides.

### Step 3. Isolate the unknown variable.

Since division is the inverse operation of multiplication, we divide both sides by the number the variable is multiplied by.

If we divide by a negative number, we need to flip the inequality symbol.

LESSON

— Solving Linear Inequalities

PRACTICE

— Solving Linear Inequalities

CONCLUSION

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