Solving Linear Equations: Find The Value Of X

Hey guys! Today, we're going to dive into solving some simple linear equations. Don't worry, it's not as scary as it sounds. We'll break it down step by step so you can easily find the value of x in each equation. Grab your pencils, and let's get started!

1. Solve for x in $5x + 10 - 2x = 40$

Okay, let's tackle the first equation: $5x + 10 - 2x = 40$. The goal here is to isolate x on one side of the equation. First, we need to simplify the left side by combining like terms. We have $5x$ and $-2x$, which combine to give us $3x$. So, the equation becomes:

$3x + 10 = 40$

Now, we want to get rid of that $+10$ on the left side. To do this, we subtract $10$ from both sides of the equation. Remember, whatever you do to one side, you have to do to the other to keep the equation balanced:

$3x + 10 - 10 = 40 - 10$

This simplifies to:

$3x = 30$

Finally, to solve for x, we need to divide both sides by $3$:

$3x / 3 = 30 / 3$

Which gives us:

$x = 10$

So, for the first equation, $x = 10$. Easy peasy!

2. Solve for x in $6x + 10 - 2x = 42$

Next up, we have the equation: $6x + 10 - 2x = 42$. Just like before, let's start by simplifying the left side. Combine the x terms: $6x - 2x = 4x$. The equation now looks like this:

$4x + 10 = 42$

Now, we need to isolate the term with x. Subtract $10$ from both sides:

$4x + 10 - 10 = 42 - 10$

This simplifies to:

$4x = 32$

To solve for x, divide both sides by $4$:

$4x / 4 = 32 / 4$

Which gives us:

$x = 8$

So, for the second equation, $x = 8$. Keep up the great work!

3. Solve for x in $2x + 20 - x = 60$

Here's the third equation: $2x + 20 - x = 60$. Again, simplify the left side by combining the x terms: $2x - x = x$. The equation becomes:

$x + 20 = 60$

To isolate x, subtract $20$ from both sides:

$x + 20 - 20 = 60 - 20$

This simplifies to:

$x = 40$

So, for the third equation, $x = 40$. You're getting the hang of it!

4. Solve for x in $8x + 10 - 4x = 18$

Now, let's solve the fourth equation: $8x + 10 - 4x = 18$. Combine the x terms on the left side: $8x - 4x = 4x$. The equation becomes:

$4x + 10 = 18$

Subtract $10$ from both sides to isolate the term with x:

$4x + 10 - 10 = 18 - 10$

This simplifies to:

$4x = 8$

Divide both sides by $4$ to solve for x:

$4x / 4 = 8 / 4$

Which gives us:

$x = 2$

So, for the fourth equation, $x = 2$. Nice job!

5. Solve for x in $6x + 10 - 3x = 55$

Time for the fifth equation: $6x + 10 - 3x = 55$. Combine the x terms on the left side: $6x - 3x = 3x$. The equation becomes:

$3x + 10 = 55$

Subtract $10$ from both sides:

$3x + 10 - 10 = 55 - 10$

This simplifies to:

$3x = 45$

Divide both sides by $3$ to solve for x:

$3x / 3 = 45 / 3$

Which gives us:

$x = 15$

So, for the fifth equation, $x = 15$. You're halfway there!

6. Solve for x in $4x + 12 - 2x = 16$

Let's move on to the sixth equation: $4x + 12 - 2x = 16$. Combine the x terms on the left side: $4x - 2x = 2x$. The equation becomes:

$2x + 12 = 16$

Subtract $12$ from both sides to isolate the term with x:

$2x + 12 - 12 = 16 - 12$

This simplifies to:

$2x = 4$

Divide both sides by $2$ to solve for x:

$2x / 2 = 4 / 2$

Which gives us:

$x = 2$

So, for the sixth equation, $x = 2$.

7. Solve for x in $6x + 16 - 2x = 28$

Seventh equation coming up: $6x + 16 - 2x = 28$. Combine the x terms on the left side: $6x - 2x = 4x$. The equation becomes:

$4x + 16 = 28$

Subtract $16$ from both sides to isolate the term with x:

$4x + 16 - 16 = 28 - 16$

This simplifies to:

$4x = 12$

Divide both sides by $4$ to solve for x:

$4x / 4 = 12 / 4$

Which gives us:

$x = 3$

So, for the seventh equation, $x = 3$.

8. Solve for x in $9x + 12 - 3x = 72$

Equation number eight: $9x + 12 - 3x = 72$. Combine the x terms on the left side: $9x - 3x = 6x$. The equation becomes:

$6x + 12 = 72$

Subtract $12$ from both sides:

$6x + 12 - 12 = 72 - 12$

This simplifies to:

$6x = 60$

Divide both sides by $6$ to solve for x:

$6x / 6 = 60 / 6$

Which gives us:

$x = 10$

So, for the eighth equation, $x = 10$.

9. Solve for x in $3 + 6x - 2 = 31$

Ninth equation time: $3 + 6x - 2 = 31$. First, combine the constants on the left side: $3 - 2 = 1$. So the equation becomes:

$6x + 1 = 31$

Subtract $1$ from both sides:

$6x + 1 - 1 = 31 - 1$

This simplifies to:

$6x = 30$

Divide both sides by $6$ to solve for x:

$6x / 6 = 30 / 6$

Which gives us:

$x = 5$

So, for the ninth equation, $x = 5$.

10. Solve for x in $7 + 2x - 1 = 26$

Last but not least, the tenth equation: $7 + 2x - 1 = 26$. Combine the constants on the left side: $7 - 1 = 6$. The equation becomes:

$2x + 6 = 26$

Subtract $6$ from both sides:

$2x + 6 - 6 = 26 - 6$

This simplifies to:

$2x = 20$

Divide both sides by $2$ to solve for x:

$2x / 2 = 20 / 2$

Which gives us:

$x = 10$

So, for the tenth equation, $x = 10$.

Conclusion

And there you have it! We've solved all ten equations for x. Hopefully, this step-by-step guide has made the process clear and easy to understand. Remember, the key is to simplify, isolate the variable, and keep the equation balanced. Keep practicing, and you'll become a pro at solving linear equations in no time! Great job, guys!