**Equations with distributive property on both sides :**

The Distributive Property can be useful in solving equations.

In this section, we are going to see, how distributive property can be used to solve equations.

**Example 1 :**

Solve : 4(x - 3) = 3(2 + x)

**Solution :**

**Step 1 : **

Use the Distributive Property.

Distribute 4 to the terms within the parentheses on the left side and 3 to the terms within the parentheses on the right side.

4x - 12 = 6 + 3x

**Step 2 : **

Use inverse operations to solve the equation.

Add 12 to both sides.

aaaaaaaaaaaaaaaaaa 4x - 12 = 6 + 3xaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa + 12 + 12 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa 4x = 18 + 3x aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa

Subtract 3x from both sides.

aaaaaaaaaaaaaaaaaa 4x = 18 + 3x aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa- 3x - 3x aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa x = 18 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaa

**Example 2 :**

Solve : 7n/10 + 3/2 = 3n/5 + 2

**Solution :**

**Step 1 : **

Find the least common multiple of the denominators (10, 2 and 5).

LCM = 5 x 2 x 1 x 1 x 1

LCM = 10

**Step 2 : **

Multiply both sides of the equation by 10.

10(7n/10 + 3/2) = 10(3n/5 + 2)

Use distributive property.

10(7n/10) + 10(3/2) = 10(3n/5) + 10(2)

Simplify.

7n + 5(3) = 2(3n) + 20

7n + 15 = 6n + 20

**Step 3 :**

Use inverse operations to solve for "n".

Subtract 15 from both sides.

aaaaaaaaaaaaaaaa 7n + 15 = 6n + 20 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 15 - 15 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 7n = 6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa

Subtract 6n from both sides.

aaaaaaaaaaaaaaaa 7n = 6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -6n -6n aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -------------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa n = 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -------------------- aaaaaaaaaaaaaaaa

**Example 3 :**

Solve : 0.7n + 0.33 = 0.3n + 0.5

**Solution :**

**Step 1 :**

In the second term 0.33 on the left side, we have two digits (more number of digits) after the decimal.

So, multiply both sides of the equation by 10² ( = 100).

100(0.7n + 0.33) = 100(0.3n + 0.5)

Use the Distributive Property.

100(0.7n) + 100(0.33) = 100(0.3n) + 100(0.5)

70n + 33 = 30n + 50

**Step 2 :**

Subtract 33 from both sides.

aaaaaaaaaaaaaaaa 70n + 33 = 30n + 50 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa - 33 - 33 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 70n = 30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa

Subtract 30n from both sides.

aaaaaaaaaaaaaaaa 70n = 30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaa - 30n = -30n aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa 40n = 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa

Divide both sides by 40.

40n/40 = 17/40

n = 0.425

After having gone through the stuff given above, we hope that the students would have understood "Equations with distributive property on both sides".

Apart from the stuff given above, if you want to know more about "Equations with distributive property on both sides", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**