How do you solve and graph #abs(-4y-3)

Question

How do you solve and graph #abs(-4y-3)<13#?

Isaiah Anthony · Accepted Answer

It's about knowing the meaning of 'absolute value' or in other words the distance from zero in a axis.

So let's first look a simple example. How do we figure out the value of x for which the absolute value of x+3 is greater than 6. Making this in mathematical format, the question becomes: #abs(x+3)>6# If #abs(x+3)=6#, what would be the value of x? It would be either #x+3=6# or #x+3=-6#...since if #abs(x)=6# it actually means the distance from x to zero is 6 units. On a axis x could be either -6 or 6, so x could attain a distance of 6. Know let's go back to your question i.e #abs(-4y-3)<13#. As we seen before here instead of just a single variable like x or y we have an expression. So instead of the variable being the distance from zero here the expression's value is the distance from zero. Know the expression #-4y-13# would have a distance of 13 from zero. So again either #-4y-13# or #-(4y-13)#, so the expression #-4y-13# could attain a distance of 13. Expressing mathematically: #-4y-13<13# or #-4y+13<13# #-4y<26# or #-4y<0# #y> -26/4# or #y>0# which would be the solution.

Jace Anderson · Answer

undefined To solve and graph the inequality abs(-4y-3)<13: 1. Rewrite the absolute value inequality as two separate inequalities: -4y - 3 < 13 and -4y - 3 > -13 2. Solve each inequality separately: For -4y - 3 < 13: -4y < 13 + 3 -4y < 16 y > -4 For -4y - 3 > -13: -4y > -13 + 3 -4y > -10 y < 2.5 3. Combine the solutions: -4 < y < 2.5 4. Graph the solution on a number line: -4---o----------------------o---2.5 -4 2.5 The open circles represent that the endpoints are not included in the solution set, and the line segment between them indicates the values of y that satisfy the original inequality.

How do you solve and graph #abs(-4y-3)&lt;13#?

How do you solve and graph #abs(-4y-3)<13#?