Solve the equation. Check the solution.EXAMPLE 1Solve x − 7 = 10 for x.SolutionTo solve fo...

Solve the equation. Check the solution.

EXAMPLE 1

Solve x − 7 = 10 for x.

Solution

To solve for x, we want x alone on one side of the equation. To do this, we add 7 to both sides of the equation.

The solution of the equation x = 17 is obviously 17. Since we are writing equivalent equations, the solution of the equation x − 7 = 10 is also 17.

Check: To check, replace x with 17 in the original equation.

Since the statement is true, 17 is the solution.

EXAMPLE 2

Solve y + 0.6 = −1.0 for y.

Solution

To get y alone on one side of the equation, subtract 0.6 from both sides of the equation.

Check: To check the proposed solution, −1.6, replace y with −1.6 in the original equation.

The solution is −1.6.

EXAMPLE 3

Solve: 2x + 3x − 5 + 7 = 10x + 3 − 6x − 4

Solution

First we simplify both sides of the equation.

Next, we want all terms with a variable on one side of the equation and all numbers on the other side.

Check:

The solution is −3.

EXAMPLE 4

Solve: 7 = −512a − 12 − 1 − 11a + 62.

Solution

Check to see that 8 is the solution.

EXAMPLE 5

Solve: .

Solution

To get x alone, multiply both sides of the equation by the reciprocal of , which is .

Check: Replace x with 6 in the original equation.

The solution is 6.

EXAMPLE 6

Solve: −3x = 33

Solution

Recall that −3x means −3 · x. To get x alone, we divide both sides by the coefficient of x, that is, −3.

Check:

The solution is −11.

EXAMPLE 7

Solve:

Solution

Recall that . To get y alone, we multiply both sides of the equation by 7, the reciprocal of .

Check:

The solution is 140.

EXAMPLE 8

Solve: 12a − 8a = 10 + 2a − 13 − 7

Solution

First, simplify both sides of the equation by combining like terms.

To get all terms containing a variable on one side, subtract 2a from both sides.

Check: Check by replacing a with −5 in the original equation. The solution is −5.

2x − 4 = 16