Question

Solve the system of inequalities: $4x+3\ge 2x+17,3x-5<-2$.

• A. $(-2,2)$
• B. $(-4,12)$
• C. $(-3/2,2/5)$
• D. No solution

Answer 1

Answer: (D)

No solution

Given $4x+3\ge 2x+17$

Adding $-2x$ and $-3$ on both sides, we get

$4x+3-2x-3\ge 2x+17-2x-3$

$\Rightarrow 4x-2x\ge 17-3$

$\Rightarrow 2x\ge 14$

Dividing by 2, we get

$x\ge 7$

Given $3x-5<-2$

Adding $5$ both sides we get

$3x-5+5<-2+5$

$\Rightarrow 3x<3$

Dividing by $3,$ we get

$x<1$

Then $x\ge 7$ and $x<1$ this is not possible then there is no solution of given inequalities.