Question

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

Answer 1

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:

$\frac{27}{3}<\frac{3x}{3}<\frac{36}{3}$

Solving the operations:

$9Thus we get the interval of solution for "x". In interval notation this is written as: [tex](9,12)$

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