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:

`(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.