Question

Solve the inequality show all work
5x-4<-39

Answer 1

x<−7

Explanation:

5x−4<−39

Add 4 to both sides.

5x<−39+4

Add −39 and 4 to get −35.

5x<−35

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

x< -35/5

Divide −35 by 5 to get −7.

x<−7

Answer 2

x < -7

Explanation:

You want to solve the inequality 5x -4 < -39.

Solution

Identify the term containing the variable, and the constant on that side of the equation. Add the opposite of that constant to both sides of the equation. (Variable term: 5x; constant there: -4.)

5x -4 +4 < -39 +4

5x < -35

Note that the coefficient of x is positive. Divide both sides of the equation by that number. (x coefficient: 5)

(5x)/5 < (-35)/5

x < -7

Because the number we divided by is positive, we do not need to adjust the direction of the inequality symbol. (If we multiply or divide by a negative number, the direction must be reversed.)

The solution is x < -7.

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Additional comment

Multiplication or division by a negative number changes the ordering:

1 < 2

-1 > -2 . . . . . both numbers multiplied (or divided) by -1

There are other operations you can do that change the ordering, too. This is the one most commonly encountered.