Solve the inequality and give the solution in interval notation.
-$7 x + 5 \geq 4 \text { and } 9 x - 4

Question

Solve the inequality and give the solution in interval notation.
-$7 x + 5 \geq 4 \text { and } 9 x - 4 < 9$
A) $\left( - \frac { 1 } { 7 } , \frac { 13 } { 9 } \right]$
B) $\left[ - \frac { 1 } { 7 } , \frac { 13 } { 9 } \right)$
C) $\left( - \frac { 1 } { 7 } , \frac { 5 } { 9 } \right]$
D) $\left[ - \frac { 1 } { 7 } , \frac { 5 } { 9 } \right)$

Quizplus · Accepted Answer

First, solve each inequality separately. For $7x + 5 \geq 4$, subtract 5 from both sides to get $7x \geq -1$, then divide by 7 to get $x \geq -\frac{1}{7}$. For $9x - 4 < 9$, add 4 to both sides to get $9x < 13$, then divide by 9 to get $x < \frac{13}{9}$. Combining these gives the interval $\left[ - \frac { 1 } { 7 } , \frac { 13 } { 9 } \right)$, where the square bracket indicates inclusion of $-\frac{1}{7}$ and the parenthesis indicates that $\frac{13}{9}$ is not included.

Solve the Inequality and Give the Solution in Interval Notation 7x+5≥4 and 9x−4<97 x + 5 \geq 4 \text { and } 9 x - 4 < 97x+5≥4 and 9x−4<9

Solve the Inequality and Give the Solution in Interval Notation $7 x + 5 \geq 4 \text { and } 9 x - 4 < 9$