Solve the linear inequality. Express the solution in set-builder notation.
-$6 x + 5 \geq 1$ and $7 x - 4

Question

Solve the linear inequality. Express the solution in set-builder notation.
-$6 x + 5 \geq 1$ and $7 x - 4 < 8$
A) $\left[ - \frac { 2 } { 3 } , \frac { 12 } { 7 } \right]$

B) $\left[ - \frac { 2 } { 3 } , \frac { 4 } { 7 } \right]$

C) $\left[ \frac { 2 } { 3 } , \frac { 12 } { 7 } \right]$

D) $\left[  \frac { 2 } { 3 } , \frac { 4 } { 7 } \right]$

Quizplus · Accepted Answer

For the first inequality, $6x + 5 \geq 1$, subtract 5 from both sides to get $6x \geq -4$, then divide by 6 to find $x \geq -\frac{2}{3}$. For the second inequality, $7x - 4 < 8$, add 4 to both sides to get $7x < 12$, then divide by 7 to find $x < \frac{12}{7}$. The solution in set-builder notation that satisfies both conditions is $\left[ - \frac { 2 } { 3 } , \frac { 12 } { 7 } \right]$.

Solve the Linear Inequality 6x+5≥16 x + 5 \geq 16x+5≥1 And 7x−4<87 x - 4 < 87x−4<8

Solve the Linear Inequality $6 x + 5 \geq 1$ And $7 x - 4 < 8$