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Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (\varnothing∅), leave the number line blank.34<3x+7 and 43>3x+7

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5 votes

we are given the following inequations:


\begin{gathered} 34<3x+7,\text{ and} \\ 43>3x+7 \end{gathered}

Since both inequalities contain the term "3x + 7" we can use a single inequality of the following form:


34<3x+7<43

We notice that the direction of the inequality with respect to "3x + 7" remains the same. Now, to solve for "x" we will subtract 7 from the three sides of the inequality:


34-7<3x+7-7<43-7

Solving the operations we get:


27<3x<36

Now we divide the three sides by 3:


(27)/(3)<(3x)/(3)<(36)/(3)

Solving the operations:


9Thus we get the interval of solution for

We use parenthesis because the inequality does not present an equal sign.

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