Question - Solving Absolute Value Inequalities
mathmathematical expressionsabsolute value inequalitiesinequality solutionssolving inequalities step by step
Solution:
The inequality provided in the image is $$ |u + 6| \geq 46 $$. Let's solve the inequality step by step.The absolute value inequality $$ |u + 6| \geq 46 $$ means that whatever expression is inside the absolute value signs must be either greater than or equal to 46 or less than or equal to -46. We can split this into two separate inequalities:1. $$ u + 6 \geq 46 $$2. $$ u + 6 \leq -46 $$For the first inequality, $$ u + 6 \geq 46 $$:Subtract 6 from both sides to get $$ u \geq 40 $$.For the second inequality, $$ u + 6 \leq -46 $$:Subtract 6 from both sides to get $$ u \leq -52 $$.Therefore, the solution to the inequality $$ |u + 6| \geq 46 $$ is $$ u \geq 40 $$ or $$ u \leq -52 $$. These solutions represent all the values of $$ u $$ that make the original inequality true.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com