Solving Equations by using Addition/ Subtraction: Solving an equation with fractions

Question 1

Solve for X:

$\frac{1}{8}x-\frac{2}{3}x+\frac{1}{5}x=1$

Question 2

$a+2\frac{1}{2}=4$

$a=\text{?}$

Question 3

Solve for X:

$\frac{1}{3}x-\frac{1}{2}x=3$

Question 4

Solve for X:

$\frac{2}{7}x-\frac{2}{3}x=4$

Question 5

Solve for X:

$\frac{2}{5}x+\frac{3}{4}x=1$

Examples with solutions for Solving Equations by using Addition/ Subtraction: Solving an equation with fractions

Exercise #1

Solve for X:

$\frac{1}{8}x-\frac{2}{3}x+\frac{1}{5}x=1$

Video Solution

Step-by-Step Solution

The common denominator of 8, 3, and 5 is 120.

Now we multiply each numerator by the corresponding number to reach 120 and thus cancel the fractions and obtain the following equation:

$(1\times x\times15)-(2\times x\times40)+(1\times x\times24)=1\times120$

We multiply the exercises in parentheses accordingly:

$15x-80x+24x=120$

We will solve the left side (from left to right) and will obtain:

$(15x-80x)+24x=120$

$-65x+24x=120$

$-41x=120$

We reduce both sides by $-41$

$\frac{-41x}{-41}=\frac{120}{-41}$

We find that x is equal $x=-\frac{120}{41}$

Answer

$-\frac{120}{41}$

Exercise #2

Question 1

Solve for X:

$\frac{1}{8}x+\frac{2}{3}x=3$

Question 2

$b-3\frac{4}{5}=-8\frac{3}{5}$

Question 3

Solve for X:

$-\frac{1}{4}x+\frac{2}{3}x-\frac{1}{6}x=2$

Question 4

Solve for X:

$\frac{1}{4}x-\frac{2}{3}x+\frac{1}{8}x=5$

Answer

$\frac{15}{7}$

Question 1

Solve for X:

$\frac{2}{3}x+\frac{1}{4}x-\frac{1}{5}x+\frac{1}{2}x=2$

Question 2

Solve for X:

$\frac{2}{4}x+\frac{1}{2}x+\frac{3}{8}x-\frac{1}{5}x=1$

Exercise #11

Solve for X:

$\frac{2}{3}x+\frac{1}{4}x-\frac{1}{5}x+\frac{1}{2}x=2$

Video Solution

Answer

$\frac{120}{73}$

Exercise #12

Solve for X:

$\frac{2}{4}x+\frac{1}{2}x+\frac{3}{8}x-\frac{1}{5}x=1$

Video Solution

Answer

$\frac{40}{47}$