Answer:
x = -37 7/15
Step-by-step explanation:
1. Find the terms with the variable. They are 4.3x on the left and 4.0x on the right.
2. Identify the term with the least coefficient*. It is 4.0x on the right.
3. Subtract that term from both sides of the equation.
4.3x -4.0x +19.35 = 8.11 +4.0x -4.0x
0.3x +19.35 = 8.11 . . . . . . simplify
4. Identify any constant term on the side of the equation with the variable. It is 19.35 on the left.
5. Subtract that constant from both sides of the equation.
0.3x +19.35 -19.35 = 8.11 -19.35
0.3x = -11.24 . . . . . . . simplify
6. Divide both sides of the equation by the coefficient of the variable. That coefficient is 0.3 in this equation.
(0.3x)/0.3 = (-11.24)/0.3
x = -37.466666... (repeating decimal)
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If you like, you can express the solution as a mixed number:
x = -11.24/0.30 = -1124/30 = -562/15
x = -37 7/15
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You are expected to be able to do the math using the numbers in any form they might appear: integers, mixed numbers, fractions, decimals, scientific notation. You can convert the problem here to an integer problem by multiplying both sides by 100:
430x +1935 = 811 +400x
The answer still has a fraction in it: x= -1124/30 = -37 7/15.
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* You subtract the term with the least coefficient so the variable term in the result has a positive coefficient. That may be desirable, but is not necessary. You can subtract either variable term to get the variable on one side of the equal sign. You have to pay attention to the resulting sign when you divide by the variable's coefficient.
