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Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

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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 Â· 6	= 34
2(2) + 30	= 34
34	= 34

The solution se to the equation is {6}.