Solve the inequality: -7 $\leq$ 9 - 8x < 16 - x

To solve the inequality $-7 \leq 9 - 8x < 16 - x$, we need to split it into two separate inequalities and solve them individually, then find the intersection of their solution sets.

Step 1: Solve the first part

$-7 \leq 9 - 8x$

Subtract 9 from both sides: $-7 - 9 \leq -8x$ $-16 \leq -8x$

Now, divide both sides by -8. Remember: When you divide or multiply an inequality by a negative number, the inequality sign must be reversed. $\frac{-16}{-8} \geq x$ $2 \geq x$ (or $x \leq 2$)

Step 2: Solve the second part

$9 - 8x < 16 - x$

Group the $x$ terms on one side and the constants on the other. Add $8x$ to both sides: $9 < 16 - x + 8x$ $9 < 16 + 7x$

Subtract 16 from both sides: $9 - 16 < 7x$ $-7 < 7x$

Divide both sides by 7: $-1 < x$ (or $x > -1$)

Step 3: Combine the results

We have two conditions:

1. $x \leq 2$
2. $x > -1$

Combining these, we get: $-1 < x \leq 2$

Our calculated result, $-1 < x \leq 2$, matches this option perfectly.

Exam Tip: When dealing with compound inequalities, always remember the "Golden Rule": if you multiply or divide by a negative number, flip the inequality sign immediately! It is the most common place where students lose marks in JAMB Mathematics.