Solve the compound inequality. Write the solution in interval notation.
- $8 \leq \frac { 9 } { 7 } x - 1

Question

Solve the compound inequality. Write the solution in interval notation.
-  $8 \leq \frac { 9 } { 7 } x - 1 < 17$
A)(7, 8]
B)[7, 14)
C)[7, 8)
D)(7, 14]

Quizplus · Accepted Answer

To solve the compound inequality $8 \leq \frac{9}{7}x - 1 < 17$, first solve each part separately. For the left part: $8 \leq \frac{9}{7}x - 1$, add 1 to both sides to get $9 \leq \frac{9}{7}x$. Multiply both sides by $\frac{7}{9}$ to get $7 \leq x$. For the right part: $\frac{9}{7}x - 1 < 17$, add 1 to both sides to get $\frac{9}{7}x < 18$. Multiply both sides by $\frac{7}{9}$ to get $x < 14$. Combining these gives the solution $7 \leq x < 14$, which is $[7, 14)$ in interval notation.

Solve the Compound Inequality 8≤97x−1<178 \leq \frac { 9 } { 7 } x - 1 < 178≤79​x−1<17

Solve the Compound Inequality $8 \leq \frac { 9 } { 7 } x - 1 < 17$