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At a Glance - Simplifying Equations

Sometimes parentheses make equations look more complicated than they actually are. (See how much more complicated this sentence seems?) If you simplify the expressions on each side of the equation before solving it, your life will be much easier.

Sample Problem

Solve the equation 9(x – 2) + 3 = 5(1 – x).

First, simplify each side to find an equivalent equation:

9x – 18 + 3 = 5 – 5x
9x – 15 = 5 – 5x

This looks much better. Now we solve this equation as usual:

Example 1

What's the value of x in the equation 4(1 – x) = 3(x + 1) – 2?


Exercise 1

Solve the equation 7y = -21.


Exercise 2

Solve the equation z + 2z – 3 = 4(z – 1).


Exercise 3

Solve the equation 3(y + 1) – 2(4 – 2y) = y.


Exercise 4

Solve the equation 0.5x – 2 + 0.25 = 0.25(x – 2).


Exercise 5

Solve the equation 3(1 – x) – 2(5 – 5x) = 2x + 3(1 + 5).


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