Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Certainly! Let's solve the equation step-by-step:
Given:
[tex]\[ -5(4x - 2) = -2(3 + 6x) \][/tex]
Step 1: Distribute the constants on both sides.
On the left side, distribute [tex]\(-5\)[/tex]:
[tex]\[ -5(4x - 2) = -5 \cdot 4x + (-5) \cdot (-2) = -20x + 10 \][/tex]
On the right side, distribute [tex]\(-2\)[/tex]:
[tex]\[ -2(3 + 6x) = -2 \cdot 3 + (-2) \cdot 6x = -6 - 12x \][/tex]
So now the equation looks like this:
[tex]\[ -20x + 10 = -6 - 12x \][/tex]
Step 2: Combine like terms to isolate the variable [tex]\(x\)[/tex].
First, we want to get all the terms containing [tex]\(x\)[/tex] on one side and the constant terms on the other side.
Let's add [tex]\(12x\)[/tex] to both sides to move the [tex]\(x\)[/tex] terms together:
[tex]\[ -20x + 12x + 10 = -6 - 12x + 12x \][/tex]
[tex]\[ -8x + 10 = -6 \][/tex]
Next, subtract [tex]\(10\)[/tex] from both sides to move the constants to the other side:
[tex]\[ -8x + 10 - 10 = -6 - 10 \][/tex]
[tex]\[ -8x = -16 \][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Divide both sides of the equation by [tex]\(-8\)[/tex]:
[tex]\[ \frac{-8x}{-8} = \frac{-16}{-8} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution to the equation [tex]\( -5(4x - 2) = -2(3 + 6x) \)[/tex] is:
[tex]\[ x = 2 \][/tex]
Given:
[tex]\[ -5(4x - 2) = -2(3 + 6x) \][/tex]
Step 1: Distribute the constants on both sides.
On the left side, distribute [tex]\(-5\)[/tex]:
[tex]\[ -5(4x - 2) = -5 \cdot 4x + (-5) \cdot (-2) = -20x + 10 \][/tex]
On the right side, distribute [tex]\(-2\)[/tex]:
[tex]\[ -2(3 + 6x) = -2 \cdot 3 + (-2) \cdot 6x = -6 - 12x \][/tex]
So now the equation looks like this:
[tex]\[ -20x + 10 = -6 - 12x \][/tex]
Step 2: Combine like terms to isolate the variable [tex]\(x\)[/tex].
First, we want to get all the terms containing [tex]\(x\)[/tex] on one side and the constant terms on the other side.
Let's add [tex]\(12x\)[/tex] to both sides to move the [tex]\(x\)[/tex] terms together:
[tex]\[ -20x + 12x + 10 = -6 - 12x + 12x \][/tex]
[tex]\[ -8x + 10 = -6 \][/tex]
Next, subtract [tex]\(10\)[/tex] from both sides to move the constants to the other side:
[tex]\[ -8x + 10 - 10 = -6 - 10 \][/tex]
[tex]\[ -8x = -16 \][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Divide both sides of the equation by [tex]\(-8\)[/tex]:
[tex]\[ \frac{-8x}{-8} = \frac{-16}{-8} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution to the equation [tex]\( -5(4x - 2) = -2(3 + 6x) \)[/tex] is:
[tex]\[ x = 2 \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.