How do you solve #(7-2b)/2

Question

How do you solve #(7-2b)/2<3#?

Isaiah Anthony · Accepted Answer

See the entire solution process below:

First, multiply each side of the inequality by #color(red)(2)# to eliminate the fraction while keeping the inequality balanced: #color(red)(2) xx (7 - 2b)/2 < color(red)(2) xx 3# #cancel(color(red)(2)) xx (7 - 2b)/color(red)(cancel(color(black)(2))) < 6# #7 - 2b < 6# Next, subtract #color(red)(7)# from each side of the inequality to isolate the #b# term while keeping the inequality balanced: #7 - 2b - color(red)(7) < 6 - color(red)(7)# #7 - color(red)(7) - 2b < -1# #0 - 2b < -1# #-2b < -1# Now divide each side of the inequality by #color(blue)(-2)# to solve for #b# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality sign. #(-2b)/color(blue)(-2) color(red)(>) (-1)/color(blue)(-2)# #(color(blue)(cancel(color(black)(-2)))b)/cancel(color(blue)(-2)) color(red)(>) 1/2# #b > 1/2#

Savannah Anderson · Answer

undefined To solve the inequality (7-2b)/2 < 3, you first multiply both sides of the inequality by 2 to eliminate the denominator. This gives you 7 - 2b < 6. Next, subtract 7 from both sides to isolate the variable term, yielding -2b < -1. Finally, divide both sides by -2, remembering to reverse the direction of the inequality when dividing by a negative number. This gives you b > 1/2 as the solution.

How do you solve #(7-2b)/2&lt;3#?

How do you solve #(7-2b)/2<3#?