Answer: [tex]x=-2[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}(x-10)=2x+1[/tex]
Distribute 1/4
[tex]\frac{1}{4}x-\frac{1}{4}(10)=2x+1[/tex]
[tex]\frac{1}{4}x-\frac{5}{2}=2x+1[/tex]
add 5/2
[tex]\frac{1}{4}x-\frac{5}{2}+\frac{5}{2}=2x+1+\frac{5}{2}[/tex]
[tex]\frac{1}{4}x=2x+\frac{1*2+5}{2}[/tex]
[tex]\frac{1}{4}x=2x+\frac{2+5}{2}[/tex]
[tex]\frac{1}{4}x=2x+\frac{7}{2}[/tex]
Subtract 2x
[tex]\frac{1}{4}x-2x=2x-2x+\frac{7}{2}[/tex]
[tex]\frac{1}{4}x-2x=\frac{7}{2}[/tex]
[tex]\frac{1-2*4}{4}x=\frac{7}{2}[/tex]
[tex]\frac{1-8}{4}x=\frac{7}{2}[/tex]
[tex]-\frac{7}{4} x=\frac{7}{2}[/tex]
Multiply by the negative reciprocal of -7/4 which is basically inverting the fraction -4/7
[tex](-\frac{4}{7} )-\frac{7}{4} x=\frac{7}{2}(-\frac{4}{7} )[/tex]
[tex]x=-\frac{28}{14}\\ x=-2[/tex]
