Answer: [tex]x=-44[/tex]
Step-by-step explanation:
Given the following equation:
[tex]\frac{3}{4}(\frac{1}{4}x+8)-(\frac{1}{2}x+2)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex]
You can follow these steps in order to solve for "x" and find its value:
1. You must apply the Distributive property:
[tex](\frac{1}{4}x)(\frac{3}{4})+(8)(\frac{3}{4})-\frac{1}{2}x-2=(4)(\frac{3}{8})-(x)(\frac{3}{8})-\frac{1}{4}\\\\\frac{3}{16}x+6-\frac{1}{2}x-2=\frac{3}{2}}-\frac{3}{8}x-\frac{1}{4}[/tex]
2. Add the like terms:
[tex]-\frac{5}{16}x+4=-\frac{3}{8}x+\frac{5}{4}[/tex]
3. Add [tex]\frac{3}{8}x[/tex] to both sides of the equation:
[tex]-\frac{5}{16}x+4+\frac{3}{8}x=-\frac{3}{8}x+\frac{5}{4}+\frac{3}{8}x\\\\\frac{1}{16}x+4=\frac{5}{4}[/tex]
4. Substract 4 from both sides of the equation:
[tex]\frac{1}{16}x+4-4=\frac{5}{4}-4\\\\\frac{1}{16}x=-\frac{11}{4}[/tex]
5. Finally, multiply both sides of the equation by 16. Then, you get:
[tex](16)(\frac{1}{16}x)=(-\frac{11}{4})(16)\\\\x=-44[/tex]
