Equations with Decimal Coefficients

1. Eliminate decimals by multiplying both sides of the equation by a power of 10 that will make the entire coefficients integer.

In the above example: 4.65x - 4.79 = 13.5 - 6.84x

Multiply both sides by 100: (4.65x - 4.79) × 100 = (13.5 - 6.84x) × 100

Now the equation is : 465x - 479 = 1350 – 684x

2. Get the variable terms on one side

Here add 684x both sides: 465x – 479 + 684x = 1350 – 684x + 684x

The equation is: 1149x – 479 = 1350

3. Get the constant terms on one side

Add 479 on both sides: 1149x – 479 + 479= 1350 + 479

The equation is: 1149x = 1829

4. Isolate the variable

Divide both sides by 1149: 1149x ÷ 1149 = 1829 ÷ 1149

Answer: x= 1.59

Consider further examples in solving equations with decimal coefficients:

1. Solve : 5.45 + 3t = 7.95 + t

Multiply 100 on both sides

545 + 300t = 795 + 100t

Now we have all integer coefficients

Subtract 545 from both sides

300t = 100t + 795 – 545

300t = 100t + 250

Subtract 100t from both sides

300t – 100t = 250

200t = 250

Divide both sides by 200

Hence t = $$\frac{250}{200}=\frac{5}{4}=1.25$$

2. Solve : 2.3x + 3.9 – 6.62x = 0.12

230x +390 – 662x = 12 ………. Multiply both sides by 100 to clear decimals

-432x + 390 = 12 ……….. Combine like terms

-432x = -378 ……….. Subtract 390 from both sides

X = $$\frac{378}{432}=\frac{7}{8}$$

The point to remember in solving equations with decimal coefficients is to multiply the entire equation in the beginning by 10, 100, 1000...etc to get rid of the decimals and get proper integer coefficients. After this the equation can be solved in the usual manner by bringing variable on one side and the constant to the other.

Explain Decimal Coefficients , What are Decimal Coefficients , Introduction to Decimal Coefficients