We assume that the equation is:
[tex]5x-(x+3)=3(2-2x)+x[/tex]To solve this equation, we need to solve, first, the corresponding operations:
1. We need to apply the distributive property to both sides of the equation (on the left side the number is -1):
[tex]5x-x-3=3\cdot2-3\cdot2x+x[/tex]2. Sum (algebraically) the like terms:
[tex]4x-3=6-6x+x\Rightarrow4x-3=6-5x[/tex]3. We need to add 5x to both sides of the equation (this is the addition property of equality):
[tex]4x+5x-3=6-5x+5x\Rightarrow9x-3=6[/tex]4. Add 3 to both sides of the equation (we apply the same property):
[tex]9x-3+3=6+3\Rightarrow9x=9[/tex]5. Finally, divide both sides by 9 (this is the division property of equality):
[tex]\frac{9x}{9}=\frac{9}{9}\Rightarrow x=1[/tex]We can check this result by substituting the value of x = 1 in the original equation:
[tex]5x-(x+3)=3(2-2x)+x[/tex]For x = 1, we have:
[tex]5(1)-(1+3)=3(2-2(1))+1_{}[/tex][tex]5-4=3(2-2)+1\Rightarrow1=3(0)+1\Rightarrow1=1[/tex]The last result is true. Then, we have checked that the answer is correct.
In summary, the solution for the equation is x = 1.
