Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Certainly! Let's carefully solve the equations step-by-step to understand how we would arrive at the solution.
### First Equation:
[tex]\[ 4(3x + 5) - 3 = 9x - 7 \][/tex]
1. Distribute the 4 on the left side:
[tex]\[ 4 \times 3x + 4 \times 5 - 3 = 9x - 7 \][/tex]
[tex]\[ 12x + 20 - 3 = 9x - 7 \][/tex]
2. Simplify the left side:
[tex]\[ 12x + 17 = 9x - 7 \][/tex]
3. Move the [tex]\(9x\)[/tex] term to the left side by subtracting [tex]\(9x\)[/tex] from both sides:
[tex]\[ 12x + 17 - 9x = -7 \][/tex]
[tex]\[ 3x + 17 = -7 \][/tex]
4. Move the 17 to the right side by subtracting 17 from both sides:
[tex]\[ 3x = -7 - 17 \][/tex]
[tex]\[ 3x = -24 \][/tex]
5. Divide both sides by 3:
[tex]\[ x = -8 \][/tex]
Thus, [tex]\(x = -8\)[/tex].
### Second Equation:
[tex]\[ \frac{1}{3}(5x - 9) = 2\left(\frac{1}{3}x + 6\right) \][/tex]
1. Distribute [tex]\(\frac{1}{3}\)[/tex] on the left side and distribute [tex]\(2\)[/tex] on the right side:
[tex]\[ \frac{1}{3} \times 5x - \frac{1}{3} \times 9 = 2 \times \frac{1}{3}x + 2 \times 6 \][/tex]
[tex]\[ \frac{5x}{3} - 3 = \frac{2x}{3} + 12 \][/tex]
2. Clear the fractions by multiplying every term by 3:
[tex]\[ 3 \times \left(\frac{5x}{3}\right) - 3 \times 3 = 3 \times \left(\frac{2x}{3}\right) + 3 \times 12 \][/tex]
[tex]\[ 5x - 9 = 2x + 36 \][/tex]
3. Move the [tex]\(2x\)[/tex] term to the left side by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[ 5x - 2x - 9 = 36 \][/tex]
[tex]\[ 3x - 9 = 36 \][/tex]
4. Move the [tex]\(-9\)[/tex] to the right side by adding 9 to both sides:
[tex]\[ 3x = 36 + 9 \][/tex]
[tex]\[ 3x = 45 \][/tex]
5. Divide both sides by 3:
[tex]\[ x = 15 \][/tex]
Thus, [tex]\(x = 15\)[/tex].
### Third Equation:
[tex]\[ 5(x + 7) - 3(x - 4) = 7x + 2 \][/tex]
1. Distribute the 5 and (-3) on the left side:
[tex]\[ 5 \times x + 5 \times 7 - 3 \times x + 3 \times 4 = 7x + 2 \][/tex]
[tex]\[ 5x + 35 - 3x + 12 = 7x + 2 \][/tex]
2. Combine like terms on the left side:
[tex]\[ (5x - 3x) + (35 + 12) = 7x + 2 \][/tex]
[tex]\[ 2x + 47 = 7x + 2 \][/tex]
3. Move the [tex]\(7x\)[/tex] term to the left side by subtracting [tex]\(7x\)[/tex] from both sides:
[tex]\[ 2x - 7x + 47 = 2 \][/tex]
[tex]\[ -5x + 47 = 2 \][/tex]
4. Move the 47 to the right side by subtracting 47 from both sides:
[tex]\[ -5x = 2 - 47 \][/tex]
[tex]\[ -5x = -45 \][/tex]
5. Divide both sides by -5:
[tex]\[ x = \frac{-45}{-5} \][/tex]
[tex]\[ x = 9 \][/tex]
Thus, [tex]\(x = 9\)[/tex].
Our final solutions for the given equations are:
1. [tex]\(x = -8\)[/tex]
2. [tex]\(x = 15\)[/tex]
3. [tex]\(x = 9\)[/tex]
Now let's verify which [tex]\(x\)[/tex] values are correct based on our understanding:
Reset Next doesn't specify a final result, but if we consider that we are summarizing our findings, we get:
- The first equation yields [tex]\(x = -8\)[/tex],
- The second equation yields [tex]\(x = 15\)[/tex],
- The third equation yields [tex]\(x = 9\)[/tex].
And these steps align with our computed solutions.
### First Equation:
[tex]\[ 4(3x + 5) - 3 = 9x - 7 \][/tex]
1. Distribute the 4 on the left side:
[tex]\[ 4 \times 3x + 4 \times 5 - 3 = 9x - 7 \][/tex]
[tex]\[ 12x + 20 - 3 = 9x - 7 \][/tex]
2. Simplify the left side:
[tex]\[ 12x + 17 = 9x - 7 \][/tex]
3. Move the [tex]\(9x\)[/tex] term to the left side by subtracting [tex]\(9x\)[/tex] from both sides:
[tex]\[ 12x + 17 - 9x = -7 \][/tex]
[tex]\[ 3x + 17 = -7 \][/tex]
4. Move the 17 to the right side by subtracting 17 from both sides:
[tex]\[ 3x = -7 - 17 \][/tex]
[tex]\[ 3x = -24 \][/tex]
5. Divide both sides by 3:
[tex]\[ x = -8 \][/tex]
Thus, [tex]\(x = -8\)[/tex].
### Second Equation:
[tex]\[ \frac{1}{3}(5x - 9) = 2\left(\frac{1}{3}x + 6\right) \][/tex]
1. Distribute [tex]\(\frac{1}{3}\)[/tex] on the left side and distribute [tex]\(2\)[/tex] on the right side:
[tex]\[ \frac{1}{3} \times 5x - \frac{1}{3} \times 9 = 2 \times \frac{1}{3}x + 2 \times 6 \][/tex]
[tex]\[ \frac{5x}{3} - 3 = \frac{2x}{3} + 12 \][/tex]
2. Clear the fractions by multiplying every term by 3:
[tex]\[ 3 \times \left(\frac{5x}{3}\right) - 3 \times 3 = 3 \times \left(\frac{2x}{3}\right) + 3 \times 12 \][/tex]
[tex]\[ 5x - 9 = 2x + 36 \][/tex]
3. Move the [tex]\(2x\)[/tex] term to the left side by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[ 5x - 2x - 9 = 36 \][/tex]
[tex]\[ 3x - 9 = 36 \][/tex]
4. Move the [tex]\(-9\)[/tex] to the right side by adding 9 to both sides:
[tex]\[ 3x = 36 + 9 \][/tex]
[tex]\[ 3x = 45 \][/tex]
5. Divide both sides by 3:
[tex]\[ x = 15 \][/tex]
Thus, [tex]\(x = 15\)[/tex].
### Third Equation:
[tex]\[ 5(x + 7) - 3(x - 4) = 7x + 2 \][/tex]
1. Distribute the 5 and (-3) on the left side:
[tex]\[ 5 \times x + 5 \times 7 - 3 \times x + 3 \times 4 = 7x + 2 \][/tex]
[tex]\[ 5x + 35 - 3x + 12 = 7x + 2 \][/tex]
2. Combine like terms on the left side:
[tex]\[ (5x - 3x) + (35 + 12) = 7x + 2 \][/tex]
[tex]\[ 2x + 47 = 7x + 2 \][/tex]
3. Move the [tex]\(7x\)[/tex] term to the left side by subtracting [tex]\(7x\)[/tex] from both sides:
[tex]\[ 2x - 7x + 47 = 2 \][/tex]
[tex]\[ -5x + 47 = 2 \][/tex]
4. Move the 47 to the right side by subtracting 47 from both sides:
[tex]\[ -5x = 2 - 47 \][/tex]
[tex]\[ -5x = -45 \][/tex]
5. Divide both sides by -5:
[tex]\[ x = \frac{-45}{-5} \][/tex]
[tex]\[ x = 9 \][/tex]
Thus, [tex]\(x = 9\)[/tex].
Our final solutions for the given equations are:
1. [tex]\(x = -8\)[/tex]
2. [tex]\(x = 15\)[/tex]
3. [tex]\(x = 9\)[/tex]
Now let's verify which [tex]\(x\)[/tex] values are correct based on our understanding:
Reset Next doesn't specify a final result, but if we consider that we are summarizing our findings, we get:
- The first equation yields [tex]\(x = -8\)[/tex],
- The second equation yields [tex]\(x = 15\)[/tex],
- The third equation yields [tex]\(x = 9\)[/tex].
And these steps align with our computed solutions.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
