How do you solve #12- \frac { 2} { 3} g < 24#?

Answer 1

#g > -18#

First, we need to isolate the #g# term on the left side of the inequality by subtracting #color(red)(12)# from each side of the inequality which will also maintain the balance of the inequality.

#12 - color(red)(12) - 2/3g < 24 - color(red)(12)#

#0 - 2/3g < 12#

#-2/3g < 12#

Now we need to multiply each side of the inequalty by the inverse of the #g# coefficient which is #color(blue)(-3/2)#,

However, because we are working with an inequality, whenever you multiply or divide an inequality by a negative number the rule is to reverse the inequality.

#color(blue)(-3/2) xx -2/3g color(red)(>) color(blue)(-3/2) xx 12#

#-cancel(color(blue)(3))/cancel(color(blue)(2)) xx -color(blue)(cancel(color(black)(2)))/color(blue)(cancel(color(black)(3)))g color(red)(>) -36/2#

#g > -18#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #12- \frac { 2} { 3} g &lt; 24#?

How do you solve #12- \frac { 2} { 3} g < 24#?