Question

Solve 4(7x−5)<−14−9x and write the solution using inequality notation.

Answer 1

We must solve the following inequality:

$4(7x-5)<-14-9x\text{.}$

1) First, we apply the distributive property for the multiplication on the left side:

$\begin{gathered} 4\cdot7x-4\cdot5<-14-9x, \\ 28x-20<-14-9x\text{.} \end{gathered}$

2) Now, we pass the -9x on the right as +9x on the left:

$\begin{gathered} 28x-20+9x<-14, \\ 37x-20<-14. \end{gathered}$

3) We pass the -20 on the left as +20 on the right:

$\begin{gathered} 37x<-14+20, \\ 37x<6. \end{gathered}$

4) Finally, we divide both sides by 37:

$x<\frac{6}{37}\text{.}$

Answer

x < 6/37