Answer:
-10
Step-by-step explanation:
Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.
Note that the expression in modulus can be expressed as a positive expression and negative expression.
For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;
[tex]3+4(\frac{x}{2} + 3) = 11[/tex]
On simplification;
[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]
For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;
[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]
On simplifying;
[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]
Hence her other solution of x is -10
