[tex]\text {Hello! Let's Solve this Problem!}[/tex]
[tex]\text {\underline {The First Step is to Simplify}}[/tex]
[tex]\text {2*x=2x}\\\text {2*5=10}\\\text {1/2*x=1/2x}\\\text {1/2*-4=-2}[/tex]
[tex]\text {Your New Problem Is: 2x+10=1/2x-2}[/tex]
[tex]\text {\underline {The Next Step is to Subtract 1/2x}}[/tex]
[tex]\text {2x+10-1/2x=1/2x-2-1/2x}[/tex]
[tex]\text {Your New Problem Is: 3/2x+10=-2}[/tex]
[tex]\text {\underline {The Next Step is to Subtract 10}}[/tex]
[tex]\text {3/2x+10-10=-2-10}[/tex]
[tex]\text {Your Final Problem Is: 3/2x-12}[/tex]
[tex]\text {\underline {The Final Step is to Multiply 2/3}}[/tex]
[tex]\text {2/3*3/2x=2/3*-12}[/tex]
[tex]\text {Your Answer Would Be:}[/tex]
[tex]\Huge\boxed {x=-8}[/tex]
[tex]\text {Best of Luck!}[/tex]
[tex] \huge\bf \underline{Solution:-}[/tex]
[tex]2(x + 5) = \frac{1}{2} (x - 4)[/tex]
[tex]⇒2x + 10 = \frac{x}{2} - \frac{4}{2} [/tex]
[tex]⇒2x - \frac{x}{2} = - \frac{4}{2} - 10[/tex]
[tex]⇒ \frac{4x - x}{2} = - 2 - 10[/tex]
[tex]⇒ \frac{3x}{2} = - 12[/tex]
[tex]⇒3x = - 24[/tex]
[tex]⇒x = - \frac{ 24}{3} [/tex]
[tex]⇒x = - 8[/tex]
[tex] \\ [/tex]
[tex] \sf \underline{Now, \: we \: are \: gonna \: do \: correction \: test :-} [/tex]
[tex]L.H.S. = 2 (x + 5) [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( - 8 + 5)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times ( - 3)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 6[/tex]
[tex]R.H.S = \frac{1}{2} (x - 4)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} ( - 8 - 4)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times ( - 12)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 6[/tex]
[tex] \bold{ \therefore{L.H.S = R.H.S}}[/tex]
[tex] \sf \red{Hence, \: the \: value \: of \: x \: is \: - 8. }[/tex]
