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.
−x + 4 = −24
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