Solve for X: 1/8x - 2/3x + 1/5x = 1 Linear Equation

Question

Solve for X:

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

00:00 Solve

00:04 We want to isolate the unknown X

00:08 We'll multiply by the common denominator to eliminate fractions

00:15 We'll divide 120 by each appropriate fraction

00:36 We'll solve each multiplication separately

00:50 We'll group the factors

01:01 We'll isolate the unknown X

01:15 And this is the solution to the question

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

$-\frac{120}{41}$