How do you solve an equation like 2(x – 3) = x + 4?

Answer 1

To solve the equation, start by distributing the 2 on the left-hand side:

2(x − 3) = x + 4

2x − 6 = x + 4

Next, subtract x from both sides:

x − 6 = 4

Finally, add 6 to each side:

x = 10 (ANSWER)

Answer 2

Solving Linear Equations

Example : 2(x – 3) = x + 4

This is called a linear equation, to solve a linear equation we'll follow these steps!

1. Following PEMDAS we'll start by distributing, the 2 to both values in the parenthesis.

2(x – 3) : First 2 • X = 2x : Second 2•3 = 6 : after distribution the equation looks like this :

2x – 6 = x + 4

1. Now we have to Isolate the variable (x).

2x – 6 = x + 4 : We're going to add six to each side.

2x – 6 = x + 4

+ 6 + 6

This cancels out the six on the left side of the equation and brings us to : 2x = x + 10

1. Now we have to continue to isolate the variable. To do so we will subtract x from each side.

2x = x + 10

– x – x

This brings us to

x = 10

1. Check our work: To do this we will plug the value of x (10) into the original equation.

2 • 10 = 10 + 10

20 = 20 : This statement is true, so the answer (10) is correct

All together :

2(x – 3) = x + 4

2 • x – 3 • 2 = x + 4

2x - 6 = x + 4 = 2x = x + 10

+ 6 + 6

2x = x + 10

–x –x

x = 10

Thanks for posting the question, I'm glad to help!

Answer 3

Left side Right side

2(x – 3) x + 4

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[ weight ] ================== [ weight ]

(same weight on both sides)

Step 1: Expand (remove parentheses)

2(x – 3) = 2 * x and 2 * -3 = 2x – 6

2x – 6 = x + 4

Step 2: Move x’s to one side

Subtract x from both sides:

2x – 6 – x = x + 4 – x

x – 6 = 4

Step 3: Get x alone

Add 6 to both sides:

x – 6 + 6 = 4 + 6

Answer will be:

x = 10

Answer 4

Given equation: 2(x – 3) = x + 4

Step 1: Distribute the 2 Multiply 2 by everything inside the parentheses:

1. 2(x – 3) = 2x – 6

So now the equation is: 2x – 6 = x + 4

Step 2: Get all x terms on one side Subtract x from both sides:

1. 2x – x – 6 = x – x + 4
2. x – 6 = 4

Step 3: Isolate x Add 6 to both sides:

1. x – 6 + 6 = 4 + 6
2. x = 10

Step 4: Check your answer Plug x = 10 back into the original equation:

1. Left side: 2(10 – 3) = 2(7) = 14
2. Right side: 10 + 4 = 14 ✓ (Hence proved)

Answer: x = 10

Answer 5

In order to solve an equation like 2(x - 3) = x + 4, we can start by simplifying the left side by using the distribution property to multiply 2 by x and by -3 so it becomes:

2x - 6 = x + 4

We can combine like terms. If you notice, 2x and x are like terms since they both have x raised to the power of 1 and -6 and 4 are like terms since they are constant numbers. To combine them, we need to move them on to one side. So, let combine the x's by subtracting x on both sides so it becomes:

2x - x - 6 = 4

x - 6 = 4

Remember, our purpose is to solve for x and in order to solve for x, we have to isolate x on one side. So, to isolate x, we can now add 6 on both sides which will give us:

x = 4 + 6

x = 10

So, our final answer is x = 10.

Answer 6

2 (x - 3) = x + 4

1. Whenever we have just parentheses, we multiply and distribute what is on the outside to the inside:
2. 2 (x - 3) = 2x - 6
3. Now we have the new equation 2x - 6 = x + 4. We can now proceed to solve this.
4. 2x - 6 = x + 4
5. Add six to both sides
6. 2x = x + 10
7. Subtract x from both sides
8. x = 10
9. Plug back in to verify
10. 2x - 6 = x + 4
11. 2(10) - 6 = (10) + 4
12. 20 - 6 = 10 + 4
13. 14 = 14
14. 14 = 14

Final Answer: x = 10

Answer 7

I'll walk you through solving this step by step.

Given equation: 2(x – 3) = x + 4

Step 1: Distribute the 2 Multiply 2 by everything inside the parentheses:

1. 2(x – 3) = 2x – 6

So now the equation is: 2x – 6 = x + 4

Step 2: Get all x terms on one side Subtract x from both sides:

1. 2x – x – 6 = x – x + 4
2. x – 6 = 4

Step 3: Isolate x Add 6 to both sides:

1. x – 6 + 6 = 4 + 6
2. x = 10

Step 4: Check your answer Plug x = 10 back into the original equation:

1. Left side: 2(10 – 3) = 2(7) = 14
2. Right side: 10 + 4 = 14 ✓

Answer: x = 10

The key steps for equations like this are: distribute any parentheses, collect like terms on each side, get all variables on one side and constants on the other, then isolate the variable.

Answer 8

To solve this equation, we can start by distributing the 2 on the left hand side. This means we are going to multiply each term inside the parentheses separated by addition or subtraction by 2.

2 ( x - 3) = x +4

2x - 6 = x +4

Now we want to combine like terms. We can do this by subtracting the x over to the left side of the equation and adding the 6 over to the right side of the equation.

2x - 6 - x = 4

x - 6 = 4

x = 4 + 6

x =10

We're done when we have x on one side of the equal sign by itself, so our final answer is x =10.

Answer 9

Problem:

Solve 2(x-3) = x+4

Expand the parentheses:

2(x-3) = 2x-6

So the equation becomes:

2x-6 = x+4

Get all x-terms on one side:

Subtract x from both sides

2x-x-6 = 4

x-6 = 4

Solve for x

Add 6 to both sides

x = 4+6

x = 10

Check your answer

Plug back into the original equation

2(10-3) = 10+4

2(7) = 14

14 = 14

Final answer:

x = 10

Answer 10

2(x-3) = x +4

expand left side, distribute the 2 amongst the x and -3 to get

2x-3(2) = 2x -6 = x+4

add 6 -x to both sides to get

x = 4+6

x =-10

check the answers

2(10-3) = 2(10)-6

2(7) = 20-6

14 = 14 It works

Answer 11

There are technically two ways to solve.

Forward:

2(x - 3) = x + 4 Simplify

2x - 6 = x + 4 Get like terms on opposite sides of the equal sign

2x - 6 + 6 - x = x + 4 - x + 6 Positve and negatives cancel out

2x - x = 4 + 6 Simplify

x = 10

Backward:

2(x - 3) = x + 4 Divide both sides by 2

2(x - 3) /2 = (x + 4) /2

(x - 3) = x /2 + 4 / 2 Simplify

x - 3 = 1/2x + 2 Get like terms on opposite sides of the equal sign

x - 3 + 3 - 1/2x = 1/2x + 2 -1/2x + 3 Simplify

x - 1/2x = 2 + 3 Simplify

1/2x = 5 Multiply both sides by 2

2 * 1/2x = 5 * 2 Simplify

x = 10

Both methods will get you to the same answer, but one may be faster and easier than the other, depending on the equation itself.

One method does the Order of Operations forwards, the other goes backwards. One may be preferred over the other, depending on which way you like best or which way is best suited for the equation.

Answer 12

2(x – 3) = x + 4

To solve this equation we need to first do the distributive property to get rid of the parentheses.

2(x - 3) --> 2 *x = 2x and 2 * 3 = 6 so 2(x-3) = 2x - 6

Our equation is now 2x - 6 = x + 4

Now we need to get the x terms on one side of the equal sign and constants (terms without variables) on the other side. To do this, I can I will subtract the x from both sides so it is no longer on the right side. 2x - x = x and x - x = 0

Our equation is now x - 6 = 4

The last step is to "move" the -6 to the other side so I am going to add 6 to both sides. I am adding because the operation in the equation is subtraction so I need to perform the opposite (inverse) operation to cancel it out. -6 + 6= 0 and 4 + 6=10

Final Answer: x = 10

Answer 13

Hello, thank you for taking the time to post your question!

In order to solve an equation like this you want to follow the order of operations and combine like terms! So in this case that would mean distributing the 2 to begin with, then getting the x terms on one side:

2(x - 3) = x + 4

2x – 6 = x + 4

x = 10

I hope that helps get you moving in the right direction! Feel free to reach out if you still have questions beyond that :)

Answer 14

Hi!

To solve this equation, you essentially want to:

1) distribute the 2 on the left hand side of the equation.

2(x-3) -> 2x-6

2) isolate one of the variables, moving it to the right hand side.

2x-6 = x+4 -> 2x= x+4+6 -> 2x= x +10

3) isolate the x's on the left hand side

2x = x+10 -> 2x-x = 10 -> x=10

Thus, your answer is x=10.

Answer 15

Key to finding the solution is that you must isolate x to the left side of the equation (the traditional approach). Doing this can generally be done in multiple ways. One way is not necessarily better than another way. Having this understanding keeps yo focussed on what the steps might be for any given problem.

Answer 16

An alternate way to solve this equation is to start by diving both sides by 2:

1) Equation: 2(x-3) = x+4

2) Divide both sides by 2: x-3 = 1/2x +2

3) Subtract 1/2x from both sides: 1/2x - 3 = 2

4) Add 3 to both sides: 1/2x = 5

5) Multiply both sides by 2: x = 10

6) SOLUTION: x = 10