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Solving Two-step inequalities
with work shown

3x+7<9

User Rehan Anis
by
8.8k points

1 Answer

1 vote

Answer:

x < 2/3

Explanation:

You want to solve the 2-step inequality 3x +7 < 9.

Two steps

If the coefficient of the variable is positive, the two steps to solving the inequality are identical to the two steps for solving a "2-step" equation.

Step 1:

Isolate the variable term by subtracting the unwanted constant with it.

3x +7 -7 < 9 -7

3x < 2

Step 2:

Divide by the coefficient of the variable.

3x/3 < 2/3

x < 2/3 . . . . . . the solution

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Additional comment

If the number you divide by (or multiply by) is negative, the sense of the inequality is reversed. For example, ...

-2x < 6

x > -3 . . . . . . divide by negative 2 and reverse the inequality symbol

This comes about because multiplying by a negative number changes the ordering.

-2 < -1

2 > 1

Some functions change ordering, too, so care must be taken when functions (or inverse functions) are applied to an inequality.

User Janneb
by
7.9k points

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