Solve for x: 7x-4=20x+2

Question

In this problem, you are given 7x-4=20x+2. How do you solve for x?

Answer 1

In this problem we have 7x-4 = 20x+2

step 1 Identify the x terms and the constant terms

step 2 Bring the x terms to one side and the rest to the other side

-4-2 = 20x-7x

step 3 solve this

-6 = 13x

step 4 find x now

x =- 6/13

Answer 2

To restate the problem, we want to solve for the variable x and are given the equation: 7x-4=20x+2. Because x is on both sides, we need to isolate the variable. This means x needs to be on only one side of the equation. Here's how we'd work this question out! I'm going to bold and separate each number so it's easier to read!

The Equation: 7x - 4 = 20x + 2

Option 1 Step 1: 7x - 4 - 7x = 20x + 2 - 7x --> - 4 = 13x + 2

We can isolate the variable on either side of the equation. Here, we'll subtract 7x from both sides of the equation. The 7x and -7x will cancel out on the left side, leaving us with -4 on the left side. I personally like x being on the left-hand side, so I'll rewrite the new equation as the following.

13x + 2 = -4

Option 1 Step 2: 13x + 2 - 2 = -4 - 2 --> 13x = -6

To further isolate the variable, we need to get rid of the +2 on the side of the equation with x. To do this, we subtract 2 from both sides of the equation.

Option 1 Step 3: 13x ÷ 13 = -6 ÷ 13x --> x = -6/13

The last step to getting x completely by itself is getting rid of the coefficient of 13. We do this by dividing each side of the equation by 13.

Checking our work:

To check our work and confirm that it's correct, we plug -6/13 into the original equation for x.

7x - 4 = 20x + 2

7(-6/13) - 4 = 20(-6/13) + 2

-42/13 - 4 = -120/13 + 2

-42/13 - 52/13 = -120/13 + 26/13

-94/13 = -94/13

After checking our work, we can confirm that the value of x is -6/13.

Here's the second option for solving this equation without the extended explanation.

Option 2:

7x - 4 = 20x + 2

7x - 4 - 20x = 20x + 2 - 20x --> -13x - 4 = 2

-13x - 4 + 4 = 2 + 4 --> -13x = 6

-13x ÷ -13 = 6 ÷ -13 --> x = - 6/13

x = -6/13

Answer 3

"Just move the variables to one side and the constants to the other."

7x - 4 = 20x +2 ⇒

7x - 20x = 2 + 4 ⇒

-13x = 6 ⇒

x = - 6/13

"Remember: the key to solving the equation above is that whenever you move a term (number or x) across the equals sign, its sign changes."

Answer 4

7x-4=20x+2

With questions like this, there are two main things to remember:

1 - Move the variables (in this case all components with x) to one side of the equation (traditionally the left side), and the numbers to the other side.

2 - Think of the equation like a lever where the equal sign is the pivot. Whatever operation you do to one side of the equation has to be done to the other side as well to maintain the balance as in a lever.

With the above two rules, you can solve any such question. Let me demonstrate that next.

Step 1 - Add 4 to both sides of the equation: (4) + 7x-4=20x+2 + (4)

We get: 7x = 20x + 6

Step 2 - Subtract 20x from both sides of the last equation: (-20x) + 7x = 20x + 6 (-20x)

We now have: -13x = 6

Step 3 - Divide both sides of the equation by -13: -13x / -13 = 6/-13

We get: x = -6/13

Optionally, if you also perform the division using a calculator you get; x = -0.462

Answer 5

7x - 4 = 20x + 2

To solve for x, we want to make sure all x's are on one side of the equation.

1.) Isolate all x's on the left side of the equation. Subtract 20x on both sides.

-13x - 4 = 2

2.) Add 4 to both sides.

-13x = 6

3.) Divide both sides by -13 to get x by itself.

x = - 6/13

Answer 6

I'll solve for x step by step.

Starting with: 7x - 4 = 20x + 2

Step 1: Get all x terms on one side Subtract 7x from both sides:

1. 4 = 13x + 2

Step 2: Get the constant terms on the other side Subtract 2 from both sides:

1. 6 = 13x

Step 3: Solve for x Divide both sides by 13: x = -6/13

Answer: x = -6/13

To verify:

1. Left side: 7(-6/13) - 4 = -42/13 - 52/13 = -94/13
2. Right side: 20(-6/13) + 2 = -120/13 + 26/13 = -94/13 ✓

Answer 7

I'll solve for x step by step.

Starting with: 7x - 4 = 20x + 2

Step 1: Get all x terms on one side Subtract 7x from both sides:

1. 4 = 13x + 2

Step 2: Get the constant terms on the other side Subtract 2 from both sides:

1. 6 = 13x

Step 3: Solve for x Divide both sides by 13: x = -6/13

Answer: x = -6/13

To verify:

1. Left side: 7(-6/13) - 4 = -42/13 - 52/13 = -94/13
2. Right side: 20(-6/13) + 2 = -120/13 + 26/13 = -94/13 ✓

Answer 8

7x - 4 = 20x + 2

To solve for x in this equation, we can bring the x terms on one side and the constants on the other. When we say solve for a variable such as x in this case, what we are really saying is to isolate x. If we can remember that throughout the steps, it becomes easy to solve the equation.

Step 1:

So, lets start by subtracting 7x to bring it to the other side so we end up with:

7x - 7x - 4 = 20x - 7x + 2

-4 = 13x + 2

Step 2:

Now, we can bring the constants together on one side. To do that, we can subtract by 2 on both sides:

-4 - 2 = 13x + 2 - 2

-6 = 13x

Final step:

The final step would be to divide by 13 on both sides to get x by itself:

-6/13 = 13x/13

-6/13 = x

x = -6/13

The final answer is x = -6/13

Answer 9

When you have an equation like this you want to start by combining like terms, so that would mean moving the x values to one side and the constant values to the other.

On this one that becomes

7x – 4 = 20x + 2

-13x = 6

At that point then you can divide both sides by -13 to get

x = -6/13

I hope that helps get you moving in the right direction! Feel free to message me if you have any more questions beyond that about how to apply this concept :)

Answer 10

For solving one-variable equations, we want to ISOLATE the variable.

Move x to one side (either one works). In this case, I chose left side.

7x - 4 = 20x + 2

7x - 4 - 20x = 2 ------------- move "20x" left

7x - 20x = 4 + 2 -------- move "-4" right

-13x = 6 ------------- simplify

x = -6/13 -------- solve

When moving a term across the equal sign, FLIP the sign.

Answer 11

7x -4 = 20x +2

combine like terms

20x -7x = -4-2 = -6

13x = -6

divide by 13

x = -6/13

x = 0.461538461538461538... where the 461538 repeats endlessly, forever & ever, amen, with an infinite number of decimals, halleluia or halleluja as we observe the wonders of Infinity

Answer 12

When given the equation: 7x - 4 = 20x + 2.

We will want to start by getting like terms on opposite sides of the equals sign. So have the x terms on one side and the non-variable terms on the other. We do this by doing the opposite of PEMDAS.

It's easier in this case to remove the smaller terms from the larger terms.

7x - 4 = 20x + 2

7x - 4 -2 = 20x + 2 - 2

7x - 6 = 20x

7x - 7x -6 = 20x -7x

-6 = 13x isolate x

-6/13 = 13x/13

x = -6/13

Answer 13

You want to get x by itself on one side of the equals sign:

7x - 4 = 20x + 2

-20x -20x (Step 1: get x stuff on one side)

-13x - 4 = 2 (you subtract 20x from the right so you have to also subtract from the left)

-13x - 4 = 2

+ 4 + 4 (Step 2: get everything else on the other)

-13x = 6 (same as before, you add 4 to the left so you add 4 to the right)

-13x = 6

÷ -13 ÷ -13 (Step 3: get the numbers off of x)

x = -6/13 (to get -13 off of x you need to divide by -13, but do it on both sides)

And you're left with x = -6/13

Answer 14

Step 1:

First thing that you'll want to do is get x on one side of the equation. Choose which side you want x to be isolated. In my personal experience, I've always isolated x on the side where x becomes positive rather than negative. But it honestly doesn't matter which side you have x isolated because you'll get the same answer for x either way you solve the equation.

In this equation, I am going to subtract 7x from both sides of the equations. When I do that, I will end up with this new updated equation: -4=13x+2

Step 2:

Once you have done that, you'll see that there is some variables left on the side that x is on. Get x by itself by either adding or subtracting that number on both sides of the equation to cancel out that variable on one side so that x is alone.

In this case, I will be subtracting 2 from both sides of the equation to get x by itself. When I do that, I will end up with this equation: -6=13x

Step 3:

Lastly, you finally have x by itself. But now, you have to get rid of the number attached to x by dividing both sides of the equation.

In this case, I will divide both sides by 13. That will cancel out the 13 attached to x, which gives you the answer, x=-6/13