Solve the equation.EXAMPLE 3Solve: SolutionWe begin by clearing fractions. To do this, we...

Solve the equation.

EXAMPLE 3

Solve:

Solution

We begin by clearing fractions. To do this, we multiply both sides of the equation by the LCD of 2 and 3, which is 6.

Step 1.

Step 2.

There are no longer grouping symbols and no like terms on either side of the equation, so we continue with Step 4.

Step 4.

Step 5. The variable is now alone, so there is no need to apply the multiplication property of equality.

Step 6. Check.

The solution is 12.

EXAMPLE 4

Solve:

Solution

We clear the equation of fractions first.

Step 1.

Step 2. Next, we use the distributive property and remove parentheses.

Step 4.

Step 5.

Step 6. To check, replace a with 0 in the original equation. The solution is 0.

EXAMPLE 5

Solve: 0.25x + 0.10(x − 3) = 0.05(22)

Solution

First we clear this equation of decimals by multiplying both sides of the equation by 100. Recall that multiplying a decimal number by 100 has the effect of moving the decimal point 2 places to the right.

0.25x + 0.10(x − 3) = 0.05(22)

Step 1.

Step 2.

Step 3.

Step 4.

Step 5.

Step 6. To check, replace x with 4 in the original equation. The solution is 4.

0.12(y − 6) + 0.06y = 0.08y − 0.70