Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} (-10x+4)=-4(-3+2x)+8[/tex]
To make things easier, let's first start by rewriting [tex]\frac{1}{2}[/tex] as a decimal:
[tex].5(-10x+4)=-4(-3+2x)+8[/tex]
Distribute [tex].5[/tex] into [tex](-10x+4)[/tex]:
[tex]-5x+2=-4(-3+2x)+8[/tex]
Distribute [tex]-4[/tex] into [tex](-3+2x)[/tex]:
[tex]-5x+2=12-8x+8[/tex]
Combine like terms:
[tex]-5x+2=20-8x[/tex]
Add [tex]8x[/tex] to both sides of the equation:
[tex]3x+2=20[/tex]
Subtract [tex]2[/tex] from both sides of the equation:
[tex]3x=18[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]3[/tex]:
[tex]x=6[/tex]
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Check your work by substituting [tex]6[/tex] into the initial equation:
[tex].5(-10(6)+4)=-4(-3+2(6))+8[/tex]
[tex].5(-60+4)=-4(-3+12)+8[/tex]
[tex]-30+2=12-48+8[/tex]
[tex]-28=-28[/tex]
The answer is correct!
