Question

I need help. I just started algebra and have no idea what I'm doing

Answer 1

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

`2(x+1)-3(x-2)=x-6`

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.

`\begin{gathered} 2x+2-3x+6=x-6 \\ \text{Because -3}\cdot-2=6 \end{gathered}`

2.Operate like terms.

`\begin{gathered} 2x+2-3x+6=x-6 \\ -x+8=x-6 \end{gathered}`

3.Group the terms with x on one side of the equal and the independent terms on the other side

`\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}`

4. Clear the unknown.

`\begin{gathered} \text{ Divide both sides of the equation by 2} \\ (14)/(2)=(2x)/(2) \\ 7=x \end{gathered}`

Example 2

`(x+1)/(6)-(3(x-2))/(8)=x-6`

1. Apply distributive property

`(x+1)/(6)-(3x-6)/(8)=x-6`

Remove the denominators by multiplying both members by the least common multiple of the denominators

`\begin{gathered} 24((x+1)/(6)-(3x-6)/(8))=24(x-6) \\ 4(x+1)-3(3x-6)=24(x-6) \\ 4x+4-9x+18=24x-144 \end{gathered}`

2. Operate like terms.

`-5x+22=24x-144`

3.Group the terms with x on one side of the equal and the independent terms on the other side

`\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}`

4. Clear the unknown.

`\begin{gathered} \text{ Divide both sides of the equation by }29 \\ (166)/(29)=(29x)/(29) \\ (166)/(29)=x \end{gathered}`

Example 3

`2(1+2x)=10`

1. Apply distributive property

`\begin{gathered} 2(1+2x)=2\cdot1+2\cdot2x=2+4x \\ \text{So, you have} \\ 2(1+2x)=10 \\ 2+4x=10 \end{gathered}`

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

`\begin{gathered} 2+4x=10 \\ \text{Subtract 2 from both sides of the equation} \\ 2+4x-2=10-2 \\ 4x=8 \end{gathered}`

4. Clear the unknown.

`\begin{gathered} \text{ Divide both sides of the equation by }4 \\ (4x)/(4)=(8)/(4) \\ x=2 \end{gathered}`