Solve for X in -8x + 3 + 1/5 = -7x + 5(1-x): Linear Equation Challenge

Video Solution

Solution Steps

00:00 Find X

00:03 Group like terms

00:11 Expand brackets properly, multiply by each term

00:25 Group like terms

00:28 Arrange the equation so that one side contains only the unknown X

00:49 Group like terms

00:52 Find the common denominator

00:59 Isolate X

01:05 Make sure to multiply numerator by numerator and denominator by denominator

01:08 And this is the solution to the problem

Step-by-Step Solution

To solve the equation $-8x + 3 + \frac{1}{5} = -7x + 5(1-x)$ , follow these steps:

Step 1: Simplify the right-hand side by distributing the 5: $-7x + 5(1-x) = -7x + 5 - 5x$ .
Step 2: This leads to $-8x + 3 + \frac{1}{5} = -12x + 5$ .
Step 3: Combine like terms on both sides. The left simplifies to $-8x + \frac{16}{5}$ and the right side already simplified as stated.
Step 4: Move all terms involving $x$ to one side, and constants to the other: Add $12x$ to both sides to get $12x - 8x = 5 - \frac{16}{5}$ .
Step 5: Simplify the equation: $4x = \frac{25}{5} - \frac{16}{5} = \frac{9}{5}$ .
Step 6: Solve for $x$ by dividing both sides by 4: $x = \frac{9}{20}$ .

Therefore, the solution to the problem is $x = \frac{9}{20}$ .