Video: Solve Linear Inequalities

Solve 7 ≀ 2π‘₯ + 1.

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Video Transcript

Solve seven is less than or equal to two π‘₯ plus one.

In order to solve any inequality, we do so in the same way as we would solve an equation. In this case, the equation seven is equal to two π‘₯ plus one. In this case, in order to solve the inequality, we firstly subtract one from both sides of the equation. Seven minus one is equal to six. On the right-hand side, one minus one is equal to zero. So we’re left with two π‘₯. Our next and final step is to divide both sides of the inequality by two. Six divided by two is equal to three. And two π‘₯ divided by two is equal to π‘₯.

The solution to the inequality, seven is less than or equal to two π‘₯ plus one, is three is less than or equal to π‘₯. This can be written in one of two ways. Either three is less than or equal to π‘₯ or π‘₯ is greater than or equal to three. We could also write this in set notation so that π‘₯ could take any value from three up to infinity. We have a square bracket on the three as it could be equal to three and a curve bracket or parentheses on the infinity as it can never equal or reach infinity.

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