Question

Consider the following inequality:2(4x - 2) > 2x + 14Step 1 of 2: Write the solution using interval notation.

Answer 1

We have the next inequality

$2(4x-2)>2x+14$

And we must solve it

To solve the inequality

1. we must expand the terms

$\begin{gathered} 2\cdot4x-2\cdot2>2x+14 \\ 8x-4>2x+14 \end{gathered}$

2. we must add 4 to both sides

$\begin{gathered} 8x-4+4>2x+14+4 \\ 8x>2x+18 \end{gathered}$

3. we must subtract 2x from both sides

$\begin{gathered} 8x-2x>2x-2x+18 \\ 6x>18 \end{gathered}$

4. we must divide both sides by 6

$\begin{gathered} \frac{6x}{6}>\frac{18}{6} \\ x>3 \end{gathered}$

Finally, writing the solution using interval notation

$(3,\infty)$

ANSWER:

(3, ∞)