Chapter 0.6, Problem 17E

To determine

To solve the equation $2z-9<7z+1$

Answer to Problem 17E

  $z>-2$

Explanation of Solution

Given Information: $2z-9<7z+1$

Formula Used : Linear inequality with one variable

Calculation:

Given equation is

  $2z-9<7z+1$

To isolate the variable z, subtract 7z from both sides-

  $2z-7z-9<7z-7z+1$

This gives

  $-5z-9<1$

To isolate the variable z, adding 9 both sides-

  $-5z-9+9<1+9$

This gives-

  $-5z<10$

To isolate the variable z, divide by 5 both sides-

  $-\frac{5}{5}z<\frac{10}{5}$

This gives-

  $-z<2$

To isolate the variable b, multiply by $-1$ both sides and the inequality sign changes-

  $z>-2$

Hence the final answer is,

  $z>-2$