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This lesson shows you some examples on solving linear equations.

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To solve a linear equation, our objective is to find what value x is equals to.

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Now, Let's solve, 2x -1 = 5 + 4x.

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Since our objective is to find what is x equals to. we need to put all the terms with x, on on one side of the equation, usually, on the Left hand side.

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We can do so by removing +4x. To do so, we add -4x to both sides of the equation.

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The equation now becomes 2x -1 -4x = 5.

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Now, notice that we also need to remove negative 1? To do so, we add +1 to both sides of the equation.

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The equation becomes 2x -4x = 5 + 1.

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Alright, we now add the like terms together.

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Adding 2x with -4x gives -2x.

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Adding 5 with 1 gives 6.

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Now, notice that to find x, we need to remove -2 from -2x.

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We can do so by dividing both sides of the equation by -2. So, we get x = +6/-2

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Finally, we can solve for x by dividing +6 with -2. This gives x = -3.

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Next example on solving linear equations, let's solve 2(2x -1) = 2x +8.

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First, we need to remove the brackets.

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2 multiply by 2x gives +4x. 2 multiply by -1 gives negative 2. Now, let's put these terms back into the equation.

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Now, we can remove 2x by adding -2x to both sides of the equation.

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This gives +4x -2 -2x = +8.

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Now, we can remove -2 by adding +2, to both sides of the equation.

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This gives +4x -2x = +8 + 2.

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We can simply this equation by adding 4x and -2x . This gives +2x.

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Now, add +8 with +2. This gives +10.

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To find x, we need to remove +2 from +2x. We can do so by dividing both sides of the equation by +2.

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The equation becomes x = +10/+2. Now, we divide +10 with +2. This gives 5.

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So, the answer is x = 5.

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Next example on solving linear equations. Let's solve. 2 (x +1) = 5 – 3(x -1).

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First, we need to remove the brackets in this equation. Let's start with 2 bracket x+1.

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2 multiply by x gives 2x. 2 multiply by +1 gives +2. Let's put these terms back.

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Now, let's remove the brackets in -3(x -1).

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-3 multiply by x gives -3x. -3 multiply by -1 gives +3. Let's put these terms back.

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Now, we need to remove -3x from the Right Hand Side. To do so, we add +3x to both sides of the equation.

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By doing so, the equation becomes 2x +2 +3x = 5 +3.

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We can remove +2 by adding -2 to both sides of the equation. The equation now becomes 2x +3x = 5 +3 -2.

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Now, we simplify the equation by adding 2x with 3x. This gives +5x

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3 minus 2 gives 1. 5 plus 1 gives 6.

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Now, to get x, we need to remove +5. We can do so by dividing +5 to both sides of the equation.

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This gives, x = +6 / +5.

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Now, since 6 divides by 5 is not an integer, we can leave the answer in the form of fraction.

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So, the answer is x = 6/5.

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Final example on solving linear equations, let's simplify x/4 + 2 = x -1.

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Now, we can remove +2 by adding -2 to both sides of the equation.

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The equation now becomes, x/4 = x -1 -2.

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Now, we can add -1 and -2. This gives -3.

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It is easier to solve this equation if we remove the denominator, 4, from this equation.

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We can do so by multiplying both sides of the equation by 4.

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The equation now becomes x = 4(x -3). Remember to put brackets around the terms when multiplying.

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To proceed, we need to remove these brackets.

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4 multiply by x gives 4x. 4 multiply by -3 gives -12. Let's put back these terms.

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We can remove 4x by adding both sides of the equation by - 4x. This gives x -4x = -12.

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Now, we can simplify the equation by adding x with -4x. This gives negative 3x.

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To get what is x equals to, we need to remove -3 from -3x.

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To do so, we divide both sides of the equation by -3.

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The equation now becomes, x = -12/ -3.

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Dividing -12 with -3 gives 4 . So, the answer is x = 4.

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That is all for this lesson on on solving linear equations. Try out the practice questions to reinforce your understanding.