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To solve a linear equation, we must simplify the equation to a binomial. Then we can isolate the variable on one side to get the answer. Examples are below
A little intro, maybe the derivation of a formula or something on how they are used
Solve for \(x\) in the following equation $$4(x+3) - 2(x-1) = 24$$
First, we need to simplify this expression down into a binomial, using the distributive property, and then comining like terms $$4x + 12 - 2x +2 = 24$$ $$2x +14 = 24$$ We can now subtract 14 from both sides $$2x+14-14 = 24-14$$ $$2x = 10$$ Next we can divide both sides by \(2\) $$\frac{2x}{2} = \frac{10}{2}$$ $$x=5$$
The process stays the same if there are \(x\) terms on both sides, as you will see in the next eample
Solve for \(x\) in the following equation: $$8x-2 = 3(2x+4) - 5x$$
First, we can simplify the right side of the equation $$8x-2 = 6x +12 - 5x$$ $$8x-2 = x+12$$ Next, we can shift the \(x\) term to the left side $$8x-2-x = x-x+12$$ $$7x-2 = 12$$ Next, using the same method, we can shift the negative two to the other side $$7x-2+2 = 12+2$$ $$7x=14$$ Then, we can divide both sides by \(7\) $$\frac{7x}{7} = \frac{14x}{7}$$ $$x = 2$$
Conlcusion:
Many future lessons will build off of these problems, so it is important to completely master them