Respuesta :
In general, to solve a first-degree equation, the following steps can be followed:
1. Apply distributive property (if necessary)
2. Operate like terms.
3.Group the terms with x on one side of the equal and the independent terms on the other side
4. Clear the unknown.
Example 1
[tex]2(x+1)-3(x-2)=x-6[/tex]1. Apply distributive property
Note: Distributive Property says that the sum of two or more addends multiplied by a number gives the same answer as distributing the multiplier, multiplying each addend separately, and adding the products together.
[tex]\begin{gathered} 2x+2-3x+6=x-6 \\ \text{Because -3}\cdot-2=6 \end{gathered}[/tex]2.Operate like terms.
[tex]\begin{gathered} 2x+2-3x+6=x-6 \\ -x+8=x-6 \end{gathered}[/tex]3.Group the terms with x on one side of the equal and the independent terms on the other side
[tex]\begin{gathered} -x+8=x-6 \\ \text{Add x to both sides of the equation} \\ -x+8+x=x-6+x \\ 8=2x-6 \\ \text{Add 6 to both sides of the equation} \\ 8+6=2x-6+6 \\ 14=2x \end{gathered}[/tex]4. Clear the unknown.
[tex]\begin{gathered} \text{ Divide both sides of the equation by 2} \\ \frac{14}{2}=\frac{2x}{2} \\ 7=x \end{gathered}[/tex]Example 2
[tex]\frac{x+1}{6}-\frac{3(x-2)}{8}=x-6[/tex]1. Apply distributive property
[tex]\frac{x+1}{6}-\frac{3x-6}{8}=x-6[/tex]Remove the denominators by multiplying both members by the least common multiple of the denominators
[tex]\operatorname{lcm}(6,8)=24[/tex][tex]\begin{gathered} 24(\frac{x+1}{6}-\frac{3x-6}{8})=24(x-6) \\ 4(x+1)-3(3x-6)=24(x-6) \\ 4x+4-9x+18=24x-144 \end{gathered}[/tex]2. Operate like terms.
[tex]-5x+22=24x-144[/tex]3.Group the terms with x on one side of the equal and the independent terms on the other side
[tex]\begin{gathered} \text{Add 5x to both sides of the equation} \\ -5x+22+5x=24x-144+5x \\ 22=29x-144 \\ \text{Add 144 to both sides of the equation} \\ 22+144=29x-144+144 \\ 166=29x \end{gathered}[/tex]4. Clear the unknown.
[tex]\begin{gathered} \text{ Divide both sides of the equation by }29 \\ \frac{166}{29}=\frac{29x}{29} \\ \frac{166}{29}=x \end{gathered}[/tex]Example 3
[tex]2(1+2x)=10[/tex]1. Apply distributive property
[tex]\begin{gathered} 2(1+2x)=2\cdot1+2\cdot2x=2+4x \\ \text{So, you have} \\ 2(1+2x)=10 \\ 2+4x=10 \end{gathered}[/tex]2. Operate like terms.
On the left side and on the right side the similar terms are already operated.
3.Group the terms with x on one side of the equal and the independent terms on the other side
[tex]\begin{gathered} 2+4x=10 \\ \text{Subtract 2 from both sides of the equation} \\ 2+4x-2=10-2 \\ 4x=8 \end{gathered}[/tex]4. Clear the unknown.
[tex]\begin{gathered} \text{ Divide both sides of the equation by }4 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}[/tex]
