{"question":{"question":{"content":"**Which graph represents the solution set of this inequality?** $\qquad 4x+11 < -21$ [[☃ radio 1]]","images":{"https://ka-perseus-graphie.s3.amazonaws.com/9ffc48c00fbd9687399c0005d92d6c3aa6ae5332.png":{"width":460,"height":80},"https://ka-perseus-graphie.s3.amazonaws.com/e4a94128fcf7b0c1cd7d11e6516edb9575d7cfc0.png":{"width":460,"height":80},"https://ka-perseus-graphie.s3.amazonaws.com/ce1b524b204db097a9e721ea2cb7ef5131c4c775.png":{"width":460,"height":80},"https://ka-perseus-graphie.s3.amazonaws.com/b91b492260978d441f3ee6d7754eba2da26880dc.png":{"width":460,"height":80}},"widgets":{"radio 1":{"type":"radio","graded":true,"options":{"choices":[{"content":"![](https://ka-perseus-graphie.s3.amazonaws.com/b91b492260978d441f3ee6d7754eba2da26880dc.png)","correct":false},{"content":"![](https://ka-perseus-graphie.s3.amazonaws.com/9ffc48c00fbd9687399c0005d92d6c3aa6ae5332.png)","correct":false},{"content":"![](https://ka-perseus-graphie.s3.amazonaws.com/e4a94128fcf7b0c1cd7d11e6516edb9575d7cfc0.png)","correct":true},{"content":"![](https://ka-perseus-graphie.s3.amazonaws.com/ce1b524b204db097a9e721ea2cb7ef5131c4c775.png)","correct":false}],"randomize":false,"multipleSelect":false,"displayCount":null,"noneOfTheAbove":false,"onePerLine":true,"deselectEnabled":false},"version":{"major":0,"minor":0}}}},"answerArea":{"type":"multiple","options":{"content":"","images":{},"widgets":{}},"calculator":false},"itemDataVersion":{"major":0,"minor":1},"hints":[{"content":"Let’s start by subtracting $\blue{11}$ from both sides of the inequality: $\qquad \begin{align} 4x+11 &< -21\\ 4x+11 \blue{-11} &< -21\blue{-11}\\ 4x &< -32\\ \end{align}$","images":{},"widgets":{}},{"content":"To isolate $x$, we need to divide both sides by $\green{4}$: $\qquad\begin{align} 4x &< -32\\ \\ \dfrac{4x}{\green{4}} &< \dfrac{-32}{\green{4}}\\ \\ x &< \purple{-8}\\ \end{align}$","images":{},"widgets":{}},{"content":"To graph the inequality $x< \purple{-8}$, we first **draw a circle at $\purple{-8}$**. This circle divides the number line into two sections: one that contains solutions to the inequality and one that does not. Since the solution uses a *less than* sign, the solution does not include the point where $x= \purple{-8}$. So the **circle at $\purple{-8}$ is not filled in**. Because the solution to the inequality says that $x < \purple{-8}$, this means that solutions are numbers to the **left** of $\purple{-8}$.","images":{},"widgets":{}},{"content":"The graph that represents the solution of the inequality $x < \purple{-8}$ is shown in $\pink{\text{Pink}}$: ![](https://ka-perseus-graphie.s3.amazonaws.com/e4a94128fcf7b0c1cd7d11e6516edb9575d7cfc0.png)","images":{"https://ka-perseus-graphie.s3.amazonaws.com/e4a94128fcf7b0c1cd7d11e6516edb9575d7cfc0.png":{"width":460,"height":80}},"widgets":{}},{"content":"","images":{},"widgets":{}}]},"problemId":27489,"exerciseId":2701,"exerciseSessionId":null,"hintsEnabled":false,"readOnly":false,"submitterId":null,"checkAnswerButtonText":"Check answer","correctButtonText":"🌟 Yes! You got it!","tryAgainButtonText":"Try again","problemAiConversationId":null}

Two-step inequalities

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