2(x - 3) + 4 = 3x - 5

Question

Solve for x by simplifying both sides of the equation and isolating the variable. Show each step of your process.

Answer 1

I like to teach students to simplify the equation first by using the Distributive Property:

2(x−3)+4=3x−52(x-3)+4=3x-52(x−3)+4=3x−5

becomes

2x−6+4=3x−52x-6+4=3x-52x−6+4=3x−5

Combine like terms:

2x−2=3x−52x-2=3x-52x−2=3x−5

Then I separate the variables from the constants by moving all the variables to one side and all the numbers to the other:

−6+4+5=3x−2x-6+4+5=3x-2x−6+4+5=3x−2x

Simplify:

3=x3=x3=x, or x=3x=3x=3.

I encourage students to keep the variables together and the constants together because it helps them stay organized and reduces careless mistakes.

Answer 2

2(x - 3) + 4 = 3x - 5

1. Distribute 2 into (x-3): 2x - 6 + 4 = 3x -5 => 2x -2 = 3x - 5
2. Subtract 3x from both sides: 2x - 3x -2 = 3x - 3x - 5 => -x -2 = -5
3. Add 2 to both sides: -x -2 +2 = -5 +2 => -x = -3
4. Divide both sides by -1: -x/-1 = -3/-1 => x = 3

Job done!

Answer 3

Watch my video to see how to solve this!

Answer 4

2(x-3) + 4 = 3x - 5

2x-6+4=3x-5

5+2x-6+4=3x

5-6+4=3x-2x

-1+4=x

x=3

Answer 5

1. Start with the equation:
2. 2(x - 3) + 4 = 3x - 5
3. Distribute the 2 to both terms inside the parentheses:
4. 2x - 6 + 4 = 3x - 5
5. Combine like terms on the left side (-6 + 4):
6. 2x - 2 = 3x - 5
7. Move 2x to the right side to get x terms together:
8. -2 = x - 5
9. Add 5 to both sides to isolate x:
10. 3 = x

Final Answer: x = 3

Answer 6

When given an equation that we want to solve for the variable, we can use two methods. One uses the order of operations forwards, the other goes backwards. I've always found forward reasoning to be best and easier, but I will show you both.

Remember PEMDAS

Forwards:

2(x - 3) + 4 = 3x - 5 First, get rid of the parentheses by multiplying the coefficient by what is inside

2x - 6 + 4 = 3x - 5 Simplify where you can

2x - 2 = 3x - 5 Get like terms on opposite sides of the equal sign

2x - 2 - 2x + 5 = 3x - 5 + 5 - 2x Cancel out negative and positive like terms

-2 + 5 = 3x - 2x Simplify

3 = x

Backwards:

2(x - 3) + 4 = 3x - 5 Subtract 4 from both sides

2(x - 3) + 4 - 4 = 3x - 5 - 4 simplify where you can

2(x - 3) = 3x - 9

2(x - 3) / 2 = (3x - 9) / 2 divide both sides by 2

x - 3 = (3x - 9) / 2 Add 3 to both sides

x - 3 + 3 = (3x - 9) / 2 + 3 simplify

x = (3x - 3) / 2 Multiply both sides by 2

2 * x = (3x - 3) / 2 * 2 simplify

2x = 3x - 3 Isolate the variable

2x + 3 - 2x= 3x - 3 + 3 - 2x Cancel terms and Simplify

3 = x

Both methods will get you the right answer; one is just easier than the other.

Remember to plug your x value back into your original equation to show your proof.

Answer 7

Hello, thank you for posting your question! You want to follow the order of operations to solve this one so that would mean starting by distributing the 2 on the lefthand side

2(x – 3) + 4 = 3x – 5

From there then it’s a matter of combining like terms and simplifying down to solve!

2x – 6 + 4 = 3x – 5

2x – 2 = 3x – 5

x = 3

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

Answer 8

2(x-3) +4= 3x -5

2x-6 +4 = 3x -5

3x -2x = -2+5

x = 3

Answer 9

To solve the equation, start by using the distributive property.

Multiply 2 by both terms inside the parentheses:

That gives you 2x - 6, then add 4.

Now the left side becomes: 2x - 6 + 4, which simplifies to 2x - 2.

So the equation is now: 2x - 2 = 3x - 5.

Next, move all the x terms to one side.

Subtract 2x from both sides to get:

-2 = x - 5

Now add 5 to both sides:

-2 + 5 = x, so x = 3.

Final Answer: x = 3