Solve the Linear Equation: 6x+18+2x=6-4 Step by Step

Q: What are like terms and how do I combine them?

Like terms have the same variable with the same exponent. In $ 6x + 2x $, both terms have x to the first power, so add the coefficients: $ 6 + 2 = 8 $ to get $ 8x $.

Q: Should I simplify the right side first or the left side?

It doesn't matter which side you start with! The key is to simplify both sides completely before trying to isolate the variable. This makes the equation much easier to solve.

Q: How do I check if x = -2 is correct?

Substitute $ x = -2 $ into the original equation: $ 6(-2) + 18 + 2(-2) = 6 - 4 $. This gives $ -12 + 18 - 4 = 2 $, and $ 2 = 2 $ ✓

Linear Equations with Like Terms

$6x+18+2x=6-4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Collect like terms

00:12 Arrange the equation so that X is isolated on one side

00:20 Isolate X

00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$6x+18+2x=6-4$

Step-by-step solution

The equation we need to solve is $6x + 18 + 2x = 6 - 4$ .

Step 1: Simplify each side of the equation.
On the left side, we have two like terms involving $x$ : $6x$ and $2x$ . We can combine these terms:

$6x + 2x = 8x$ .

Thus, the equation becomes:

$8x + 18 = 6 - 4$ .

On the right side, simplify $6 - 4$ to get:

$2$ .

The equation now reads:

$8x + 18 = 2$ .

Step 2: Isolate the variable $x$ .
Subtract 18 from both sides to move the constant term on the right side:

$8x + 18 - 18 = 2 - 18$ .

This simplifies to:

$8x = -16$ .

Next, divide both sides by 8 to solve for $x$ :

$x = \frac{-16}{8}$ .

This simplifies to:

$x = -2$ .

Therefore, the solution to the equation $6x + 18 + 2x = 6 - 4$ is $x = -2$ .

Final Answer

$-2$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Add coefficients of same variables together first
Technique: Simplify both sides completely: $6x + 2x = 8x$ and $6 - 4 = 2$
Check: Substitute $x = -2$ back: $8(-2) + 18 = 2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms before solving
Don't try to isolate x without first combining 6x + 2x = 8x! This leads to messy work and calculation errors. Always simplify both sides completely by combining like terms and constants before moving to isolation steps.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

What are like terms and how do I combine them?

Like terms have the same variable with the same exponent. In $6x + 2x$ , both terms have x to the first power, so add the coefficients: $6 + 2 = 8$ to get $8x$ .

Why do I get a negative answer?

Negative solutions are completely normal! When we subtract 18 from both sides, we get $8x = -16$ . Dividing by 8 gives $x = -2$ , which is the correct answer.

Should I simplify the right side first or the left side?

It doesn't matter which side you start with! The key is to simplify both sides completely before trying to isolate the variable. This makes the equation much easier to solve.

How do I check if x = -2 is correct?

Substitute $x = -2$ into the original equation: $6(-2) + 18 + 2(-2) = 6 - 4$ . This gives $-12 + 18 - 4 = 2$ , and $2 = 2$ ✓

What if I moved terms differently?

There are multiple correct approaches! You could subtract 18 first, then combine like terms. As long as you follow the same operation on both sides, you'll get the same answer.

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