Solve the Linear Equation: 70x + 30x + 10 + 1 + 10x = 0

Q: Why do I need to combine like terms first?

Combining like terms simplifies the equation and makes it easier to solve! Instead of working with five terms, you get just two: $ 110x + 11 = 0 $.

Q: How do I know which terms are like terms?

Like terms have the same variable with the same exponent. Here: 70x, 30x, and 10x are like terms (all have x¹). Constants 10 and 1 are also like terms.

Q: Can I get a negative answer for x?

Absolutely! Negative solutions are common in algebra. $ x = -\frac{1}{10} $ is perfectly valid. Always check your work by substituting back into the original equation.

Q: Why is the answer a fraction?

When you divide -11 by 110, you get $ -\frac{11}{110} $, which simplifies to $ -\frac{1}{10} $. Many equations have fractional solutions - that's completely normal!

Linear Equations with Like Term Combining

$70x+30x+10+1+10x=0$

$x=\text{?}$

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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 terms

00:15 Arrange the equation so that one side has only the unknown X

00:22 Isolate X

00:34 Factor 110 into 11 and 10

00:42 Simplify as much as possible

00:45 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

$70x+30x+10+1+10x=0$

$x=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Combine all like terms in the equation.
Step 2: Simplify to find the value of $x$ .

Now, let's work through each step:
Step 1: The equation is $70x + 30x + 10 + 1 + 10x = 0$ . We start by combining the like terms:
$70x + 30x + 10x = 110x$ .
Thus, the equation simplifies to $110x + 10 + 1 = 0$ .

Step 2: Combine the constant terms:
$10 + 1 = 11$ .
So, the equation becomes $110x + 11 = 0$ .
Subtract 11 from both sides to isolate the term with $x$ :
$110x = -11$ .

To solve for $x$ , divide both sides by 110:
$x = -\frac{11}{110}$ .

Simplify the fraction:
$x = -\frac{1}{10}$ .

Therefore, the solution to the equation is $x = -\frac{1}{10}$ .

Final Answer

$-\frac{1}{10}$

Key Points to Remember

Essential concepts to master this topic

Combining Rule: Add coefficients of like terms: 70x + 30x + 10x = 110x
Technique: Isolate variable term first: 110x + 11 = 0 becomes 110x = -11
Check: Substitute $x = -\frac{1}{10}$ : 110(-1/10) + 11 = -11 + 11 = 0 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine all like terms before solving
Don't solve 70x + 30x + 10 + 1 + 10x = 0 without combining terms first = messy algebra and wrong answers! This creates unnecessary complexity and leads to calculation errors. Always combine all like terms (70x + 30x + 10x = 110x) and constants (10 + 1 = 11) before isolating the variable.

Practice Quiz

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$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I need to combine like terms first?

Combining like terms simplifies the equation and makes it easier to solve! Instead of working with five terms, you get just two: $110x + 11 = 0$ .

What if I forget to combine some terms?

You'll get the wrong answer! For example, if you only combine some x-terms, you might solve for the wrong value. Always identify all like terms before combining.

How do I know which terms are like terms?

Like terms have the same variable with the same exponent. Here: 70x, 30x, and 10x are like terms (all have x¹). Constants 10 and 1 are also like terms.

Can I get a negative answer for x?

Absolutely! Negative solutions are common in algebra. $x = -\frac{1}{10}$ is perfectly valid. Always check your work by substituting back into the original equation.

Why is the answer a fraction?

When you divide -11 by 110, you get $-\frac{11}{110}$ , which simplifies to $-\frac{1}{10}$ . Many equations have fractional solutions - that's completely normal!

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