Question

2 x minus 6less than7 left parenthesis x plus 2 right parenthesis

Answer 1

To solve the inequality \( 2x - 6 < 7(x + 2) \), we will first expand the right-hand side and then isolate \( x \).

1. Expand the right-hand side:

\[
7(x + 2) = 7x + 14
\]

So the inequality becomes:

\[
2x - 6 < 7x + 14
\]

2. Next, let's isolate the \( x \) terms. Subtract \( 2x \) from both sides:

\[
-6 < 7x - 2x + 14
\]

This simplifies to:

\[
-6 < 5x + 14
\]

3. Now, subtract 14 from both sides:

\[
-6 - 14 < 5x
\]

Which simplifies to:

\[
-20 < 5x
\]

4. Finally, divide each side by 5:

\[
-4 < x
\]

This can also be written as:

\[
x > -4
\]

So the solution to the inequality \( 2x - 6 < 7(x + 2) \) is:

\[
x > -4
\]