Question

StartFraction 3 left parenthesis x minus 6 right parenthesis Over 2 EndFraction
greater than or equalsStartFraction 2 x Over 7 EndFraction
minus12

The solution as an inequality is

Answer 1

To solve the inequality

\[
\frac{3(x - 6)}{2} \geq \frac{2x}{7} - 12,
\]

first, we clear the fractions by multiplying both sides by 14 (the least common multiple of 2 and 7):

\[
14 \cdot \frac{3(x - 6)}{2} \geq 14 \cdot \left(\frac{2x}{7} - 12\right).
\]

This simplifies to:

\[
7 \cdot 3(x - 6) \geq 4x - 168.
\]

Now simplify the left side:

\[
21(x - 6) \geq 4x - 168.
\]

Distributing 21 gives us:

\[
21x - 126 \geq 4x - 168.
\]

Next, isolate \(x\) by subtracting \(4x\) from both sides:

\[
21x - 4x - 126 \geq -168.
\]

This simplifies to:

\[
17x - 126 \geq -168.
\]

Now add \(126\) to both sides:

\[
17x \geq -168 + 126.
\]

Calculating the right side yields:

\[
17x \geq -42.
\]

Finally, divide both sides by 17:

\[
x \geq -\frac{42}{17}.
\]

Thus, the solution to the inequality is

\[
x \geq -\frac{42}{17}.
\]