Doug C. answered • 01/12/25
Math Tutor with Reputation to make difficult concepts understandable
Simplify each side of the equation as much as possible by removing parentheses and combining similar terms. In this case:
9x + 9 = 0
Now "drag" the constant term to the other side of the equal sign. Picture moving it, but changing its sign. You are really subtracting 9 from both sides of the equation. This is also called transposing a term.
9x = -9
Finally divide both sides of the equation by the coefficient of x (or multiply both sides by the coefficient's reciprocal).
x = -9/9
x = -1
Check:
7(-1) + 2(-1) + 9 =? 0
-7 - 2 + 9 =? 0
-9 + 9 =? 0
0 = 0 (check)
Here is a slightly more complicated example:
Solve:
3(x + 5) - 2 = 6x - 7
3x + 15 - 2 = 6x - 7 (distribute the 3)
3x + 13 = 6x - 7 (combine similar terms)
3x - 6x = -7 - 13 (transpose constant terms to one side of the equal sign and terms with x to other side)
-3x = -20 (combine similar terms)
x = -20/-3 (division property for equality)
x = 20/3
Check:
3(20/3 + 5) - 2 =? 6(20/3) - 7
20 + 15 - 2 = ? 40 - 7
35 - 2 =? 33
33 = 33
