Solve for X in 7(-2x+5)=77: Linear Equation Practice

Q: Why do I have to distribute the 7 to both terms?

The distributive property says $ a(b+c) = ab + ac $. The number outside affects everything inside the parentheses, so 7 must multiply both -2x and +5.

Q: What if the number outside is negative?

The same rule applies! If you have $ -3(2x-4) $, distribute to get $ -6x + 12 $. Remember: negative times negative equals positive.

Q: Can I solve this without distributing first?

You could divide both sides by 7 first to get $ -2x + 5 = 11 $, but distributing first is usually clearer and helps avoid mistakes with fractions.

Linear Equations with Distributive Property

Solve for x:

$7(-2x+5)=77$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Open brackets properly, multiply by each factor

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

00:25 Collect like terms

00:32 Isolate X

00:40 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$7(-2x+5)=77$

Step-by-step solution

To open parentheses we will use the formula:

$a(x+b)=ax+ab$

$(7\times-2x)+(7\times5)=77$

We multiply accordingly

$-14x+35=77$

We will move the 35 to the right section and change the sign accordingly:

$-14x=77-35$

We solve the subtraction exercise on the right side and we will obtain:

$-14x=42$

We divide both sections by -14

$\frac{-14x}{-14}=\frac{42}{-14}$

$x=-3$

Final Answer

-3

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term inside parentheses by outside coefficient
Technique: 7(-2x+5) becomes -14x+35 by distributing the 7
Check: Substitute x = -3: 7(-2(-3)+5) = 7(11) = 77 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't multiply only the first term like 7(-2x) = -14x and leave +5 unchanged = incomplete distribution! This creates equations like -14x + 5 = 77 instead of -14x + 35 = 77, giving wrong answers. Always multiply the outside number by every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I have to distribute the 7 to both terms?

The distributive property says $a(b+c) = ab + ac$ . The number outside affects everything inside the parentheses, so 7 must multiply both -2x and +5.

What if the number outside is negative?

The same rule applies! If you have $-3(2x-4)$ , distribute to get $-6x + 12$ . Remember: negative times negative equals positive.

Can I solve this without distributing first?

You could divide both sides by 7 first to get $-2x + 5 = 11$ , but distributing first is usually clearer and helps avoid mistakes with fractions.

How do I know which direction to move terms?

Move terms with variables to one side and numbers to the other. When you move a term across the equals sign, change its sign (+ becomes -, and - becomes +).

Why is my answer negative?

Negative answers are perfectly normal! In this problem, x = -3 because when you substitute it back, it makes the equation true. Don't assume answers must be positive.

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