# Multi-Step Inequalities

Multi-Step Inequalities

Tip: This isn't the place to ask a question because the teacher can't reply.

1 of 3 videos by Khan Academy

## Key Questions

• There isn't that big of a difference between solving a multi-step equation and a multi-step inequality.

When given the inequality solve as if your solving an equation but at the end there is a less than, greater than, or less than or greater than or equal to sign. One main difference is you switch the symbol when dividing by a negative.

• I would start with arranging terms so that all variables are on one side.

I hope that this was helpful.

• Solve it like a normal equation, with a few rules however.

$5 x - 4 > 21$

$5 x - 4 > 21$ (Add four to each side)

$5 x > 25$ (Divide by 5)

$x > 5$

If you have to multiply or divide by a negative, the sign flips.

$- 5 x - 4 > 21$ (Repeat the same steps)

$- 5 x > 25$ Here we have to divide by a negative, -5, so the sign flips.

$x < - 5$

• If your variable cancels out, there are two possible outcomes. Assuming you have an equation like

$x + 3 = x + 9 \to 3 = 9$

and the $x$ variable cancels out. In this case, 3 is not equal to 9 so there is no solution.
An example of the other case is

$2 x + 12 = 2 x + \left({3}^{2} + 3\right) \to 12 = 9 + 3 = 12$

Because this statement it true, that means any number could be in the place of that variable.

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