Solve for X: 3x + 2/3 = 4(x + 1/12) Linear Equation

Question

$3x+\frac{2}{3}=4(x+\frac{1}{12})$

$x=\text{?}$

00:00 Solve

00:04 Open brackets properly, multiply by each factor

00:10 We want to isolate the unknown X

00:16 Let's arrange the equation so that X is only on one side

00:47 Let's break down 12 into factors 4 and 3

00:52 Let's reduce what we can

01:04 Convert from negative to positive

01:10 And this is the solution to the question

To solve the equation $3x + \frac{2}{3} = 4 \left(x + \frac{1}{12}\right)$ , we follow these steps:

Step 1: Distribute the 4 on the right-hand side.

$4(x + \frac{1}{12}) = 4x + \frac{4}{12}$ which simplifies to $4x + \frac{1}{3}$ .

Step 2: Write down the modified equation.

The equation now reads: $3x + \frac{2}{3} = 4x + \frac{1}{3}$ .

Step 3: Rearrange the equation to collect like terms.

Subtract $3x$ from both sides: $3x + \frac{2}{3} - 3x = 4x + \frac{1}{3} - 3x$ .

This simplifies to: $\frac{2}{3} = x + \frac{1}{3}$ .

Step 4: Isolate $x$ .

Subtract $\frac{1}{3}$ from both sides: $\frac{2}{3} - \frac{1}{3} = x$ .

This simplifies to: $x = \frac{1}{3}$ .

Therefore, the solution to the equation is $\boxed{\frac{1}{3}}$ .

$\frac{1}{3}$