Math / Algebra

Question $\checkmark$ Select an answer he how $m$
Infinitely many: All real numbers
No solution One solution $+33$
Select an answer $-6(-2 x+1)-5=12 x-10$

Studdy Solution

STEP 1

What is this asking? We need to figure out how many solutions the equation $-6(-2x + 1) - 5 = 12x - 10$ has. Watch out! Don't rush!
It's easy to make mistakes with the signs when distributing.

STEP 2

1. Simplify the equation
2. Analyze the result

STEP 3

Let's distribute the $-6$ across the terms inside the parentheses.
Remember, a negative times a negative is a positive, and a negative times a positive is a negative!
So, we have $-6 \cdot -2x = 12x$ and $-6 \cdot 1 = -6$ .
Our equation becomes $12x - 6 - 5 = 12x - 10$ .

STEP 4

Now, let's combine those like terms on the left side.
We have $-6$ and $-5$ .
Adding those together gives us $-11$ .
So, our equation is now $12x - 11 = 12x - 10$ .

STEP 5

To isolate the $x$ term, we'll subtract $12x$ from both sides of the equation.
This gives us $12x - 12x - 11 = 12x - 12x - 10$ , which simplifies to $-11 = -10$ .

STEP 6

Whoa, hold on!
Does $-11$ actually equal $-10$ ?
Nope, definitely not!
This means there's no value of $x$ that will make the original equation true.

STEP 7

Since $-11$ does not equal $-10$ , there is no solution to the given equation.

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Question $\checkmark$ Select an answer he how $m$
Infinitely many: All real numbers
No solution One solution $+33$
Select an answer $-6(-2 x+1)-5=12 x-10$

Studdy Solution

STEP 1

What is this asking? We need to figure out how many solutions the equation $-6(-2x + 1) - 5 = 12x - 10$ has. Watch out! Don't rush!
It's easy to make mistakes with the signs when distributing.

STEP 2

1. Simplify the equation
2. Analyze the result

STEP 3

Let's distribute the $-6$ across the terms inside the parentheses.
Remember, a negative times a negative is a positive, and a negative times a positive is a negative!
So, we have $-6 \cdot -2x = 12x$ and $-6 \cdot 1 = -6$ .
Our equation becomes $12x - 6 - 5 = 12x - 10$ .

STEP 4

Now, let's combine those like terms on the left side.
We have $-6$ and $-5$ .
Adding those together gives us $-11$ .
So, our equation is now $12x - 11 = 12x - 10$ .

STEP 5

To isolate the $x$ term, we'll subtract $12x$ from both sides of the equation.
This gives us $12x - 12x - 11 = 12x - 12x - 10$ , which simplifies to $-11 = -10$ .

STEP 6

Whoa, hold on!
Does $-11$ actually equal $-10$ ?
Nope, definitely not!
This means there's no value of $x$ that will make the original equation true.

STEP 7

Since $-11$ does not equal $-10$ , there is no solution to the given equation.

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Question✓\checkmark✓ Select an answer he how mmmInfinitely many: All real numbersNo solution One solution +33+33+33Select an answer −6(−2x+1)−5=12x−10-6(-2 x+1)-5=12 x-10−6(−2x+1)−5=12x−10

Studdy Solution

STEP 1

What is this asking? We need to figure out how many solutions the equation −6(−2x+1)−5=12x−10-6(-2x + 1) - 5 = 12x - 10−6(−2x+1)−5=12x−10 has. Watch out! Don't rush!It's easy to make mistakes with the signs when distributing.

STEP 2

1. Simplify the equation2. Analyze the result

STEP 3

STEP 4

Now, let's **combine** those **like terms** on the left side.We have −6-6−6 and −5-5−5.Adding those together gives us −11-11−11.So, our equation is now 12x−11=12x−1012x - 11 = 12x - 1012x−11=12x−10.

STEP 5

To **isolate** the xxx term, we'll subtract 12x12x12x from both sides of the equation.This gives us 12x−12x−11=12x−12x−1012x - 12x - 11 = 12x - 12x - 1012x−12x−11=12x−12x−10, which simplifies to −11=−10-11 = -10−11=−10.

STEP 6

Whoa, hold on!Does −11-11−11 actually equal −10-10−10?Nope, definitely not!This means there's **no value** of xxx that will make the original equation true.

STEP 7

Since −11-11−11 does not equal −10-10−10, there is **no solution** to the given equation.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\checkmark$ Select an answer he how $m$
Infinitely many: All real numbers
No solution One solution $+33$
Select an answer $-6(-2 x+1)-5=12 x-10$

What is this asking? We need to figure out how many solutions the equation $-6(-2x + 1) - 5 = 12x - 10$ has. Watch out! Don't rush!
It's easy to make mistakes with the signs when distributing.

1. Simplify the equation
2. Analyze the result

Now, let's combine those like terms on the left side.
We have $-6$ and $-5$ .
Adding those together gives us $-11$ .
So, our equation is now $12x - 11 = 12x - 10$ .

To isolate the $x$ term, we'll subtract $12x$ from both sides of the equation.
This gives us $12x - 12x - 11 = 12x - 12x - 10$ , which simplifies to $-11 = -10$ .

Whoa, hold on!
Does $-11$ actually equal $-10$ ?
Nope, definitely not!
This means there's no value of $x$ that will make the original equation true.

Since $-11$ does not equal $-10$ , there is no solution to the given equation.