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Solving Linear Equations

To solve some equations, we must simplify the equation before using the properties of equality.

 

Example 1

Simplifying the equations first

Solve the equation 2(x - 4) + 5x = 34.

Solution

Before using the properties of equality, we simplify the expression on the left-hand side of the equation:

2(x - 4) + 5x = 34  
2x - 8 + 5x = 34 Distributive property
7x - 8 = 34 Combine like terms.
7x - 8 + 8 = 34 + 8 Add 8 to each side.
7x = 42 Simplify.
Divide each side by 7 to get a single x on the left side.
x = 6  

To check, we replace x by 6 in the original equation and simplify:

2(6 - 4) + 5 · 6 = 34
2(2) + 30 = 34
34 = 34

The solution se to the equation is {6}.

 
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