Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine which equation gives the value of [tex]\( x = 8 \)[/tex] when solved, we will go through each option step-by-step, solving for [tex]\( x \)[/tex].
### Option A: [tex]\(\frac{5}{2} x + \frac{7}{2} = \frac{3}{4} x + 14\)[/tex]
1. Subtract [tex]\(\frac{3}{4} x\)[/tex] from both sides:
[tex]\[ \frac{5}{2} x - \frac{3}{4} x + \frac{7}{2} = 14 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \left( \frac{5}{2} - \frac{3}{4} \right) x + \frac{7}{2} = 14 \][/tex]
[tex]\[ \frac{10}{4} x - \frac{3}{4} x + \frac{7}{2} = 14 \][/tex]
[tex]\[ \frac{7}{4} x + \frac{7}{2} = 14 \][/tex]
3. Subtract [tex]\(\frac{7}{2}\)[/tex] from both sides:
[tex]\[ \frac{7}{4} x = 14 - \frac{7}{2} \][/tex]
[tex]\[ \frac{7}{4} x = \frac{28}{2} - \frac{7}{2} \][/tex]
[tex]\[ \frac{7}{4} x = \frac{21}{2} \][/tex]
4. Multiply both sides by [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[ x = \frac{21}{2} \cdot \frac{4}{7} \][/tex]
[tex]\[ x = 3 \times 2 \][/tex]
[tex]\[ x = 6 \][/tex]
Option A does not give [tex]\( x = 8 \)[/tex].
### Option B: [tex]\(\frac{5}{4} x - 9 = \frac{3}{2} x - 12\)[/tex]
1. Subtract [tex]\(\frac{3}{2} x\)[/tex] from both sides:
[tex]\[ \frac{5}{4} x - \frac{3}{2} x - 9 = -12 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{5}{4} x - \frac{6}{4} x - 9 = -12 \][/tex]
[tex]\[ -\frac{1}{4} x - 9 = -12 \][/tex]
3. Add 9 to both sides:
[tex]\[ -\frac{1}{4} x = -12 + 9 \][/tex]
[tex]\[ -\frac{1}{4} x = -3 \][/tex]
4. Multiply both sides by [tex]\(-4\)[/tex]:
[tex]\[ x = -3 \times -4 \][/tex]
[tex]\[ x = 12 \][/tex]
Option B does not give [tex]\( x = 8 \)[/tex].
### Option C: [tex]\(\frac{5}{4} x - 2 = \frac{3}{2} x - 4\)[/tex]
1. Subtract [tex]\(\frac{3}{2} x\)[/tex] from both sides:
[tex]\[ \frac{5}{4} x - \frac{3}{2} x - 2 = -4 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{5}{4} x - \frac{6}{4} x - 2 = -4 \][/tex]
[tex]\[ -\frac{1}{4} x - 2 = -4 \][/tex]
3. Add 2 to both sides:
[tex]\[ -\frac{1}{4} x = -4 + 2 \][/tex]
[tex]\[ -\frac{1}{4} x = -2 \][/tex]
4. Multiply both sides by [tex]\(-4\)[/tex]:
[tex]\[ x = -2 \times -4 \][/tex]
[tex]\[ x = 8 \][/tex]
Option C gives [tex]\( x = 8 \)[/tex].
### Option D: [tex]\(\frac{5}{2} x - 7 = \frac{3}{4} x + 14\)[/tex]
1. Subtract [tex]\(\frac{3}{4} x\)[/tex] from both sides:
[tex]\[ \frac{5}{2} x - \frac{3}{4} x - 7 = 14 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{10}{4} x - \frac{3}{4} x - 7 = 14 \][/tex]
[tex]\[ \frac{7}{4} x - 7 = 14 \][/tex]
3. Add 7 to both sides:
[tex]\[ \frac{7}{4} x = 14 + 7 \][/tex]
[tex]\[ \frac{7}{4} x = 21 \][/tex]
4. Multiply both sides by [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[ x = 21 \times \frac{4}{7} \][/tex]
[tex]\[ x = 3 \times 4 \][/tex]
[tex]\[ x = 12 \][/tex]
Option D does not give [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
### Option A: [tex]\(\frac{5}{2} x + \frac{7}{2} = \frac{3}{4} x + 14\)[/tex]
1. Subtract [tex]\(\frac{3}{4} x\)[/tex] from both sides:
[tex]\[ \frac{5}{2} x - \frac{3}{4} x + \frac{7}{2} = 14 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \left( \frac{5}{2} - \frac{3}{4} \right) x + \frac{7}{2} = 14 \][/tex]
[tex]\[ \frac{10}{4} x - \frac{3}{4} x + \frac{7}{2} = 14 \][/tex]
[tex]\[ \frac{7}{4} x + \frac{7}{2} = 14 \][/tex]
3. Subtract [tex]\(\frac{7}{2}\)[/tex] from both sides:
[tex]\[ \frac{7}{4} x = 14 - \frac{7}{2} \][/tex]
[tex]\[ \frac{7}{4} x = \frac{28}{2} - \frac{7}{2} \][/tex]
[tex]\[ \frac{7}{4} x = \frac{21}{2} \][/tex]
4. Multiply both sides by [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[ x = \frac{21}{2} \cdot \frac{4}{7} \][/tex]
[tex]\[ x = 3 \times 2 \][/tex]
[tex]\[ x = 6 \][/tex]
Option A does not give [tex]\( x = 8 \)[/tex].
### Option B: [tex]\(\frac{5}{4} x - 9 = \frac{3}{2} x - 12\)[/tex]
1. Subtract [tex]\(\frac{3}{2} x\)[/tex] from both sides:
[tex]\[ \frac{5}{4} x - \frac{3}{2} x - 9 = -12 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{5}{4} x - \frac{6}{4} x - 9 = -12 \][/tex]
[tex]\[ -\frac{1}{4} x - 9 = -12 \][/tex]
3. Add 9 to both sides:
[tex]\[ -\frac{1}{4} x = -12 + 9 \][/tex]
[tex]\[ -\frac{1}{4} x = -3 \][/tex]
4. Multiply both sides by [tex]\(-4\)[/tex]:
[tex]\[ x = -3 \times -4 \][/tex]
[tex]\[ x = 12 \][/tex]
Option B does not give [tex]\( x = 8 \)[/tex].
### Option C: [tex]\(\frac{5}{4} x - 2 = \frac{3}{2} x - 4\)[/tex]
1. Subtract [tex]\(\frac{3}{2} x\)[/tex] from both sides:
[tex]\[ \frac{5}{4} x - \frac{3}{2} x - 2 = -4 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{5}{4} x - \frac{6}{4} x - 2 = -4 \][/tex]
[tex]\[ -\frac{1}{4} x - 2 = -4 \][/tex]
3. Add 2 to both sides:
[tex]\[ -\frac{1}{4} x = -4 + 2 \][/tex]
[tex]\[ -\frac{1}{4} x = -2 \][/tex]
4. Multiply both sides by [tex]\(-4\)[/tex]:
[tex]\[ x = -2 \times -4 \][/tex]
[tex]\[ x = 8 \][/tex]
Option C gives [tex]\( x = 8 \)[/tex].
### Option D: [tex]\(\frac{5}{2} x - 7 = \frac{3}{4} x + 14\)[/tex]
1. Subtract [tex]\(\frac{3}{4} x\)[/tex] from both sides:
[tex]\[ \frac{5}{2} x - \frac{3}{4} x - 7 = 14 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{10}{4} x - \frac{3}{4} x - 7 = 14 \][/tex]
[tex]\[ \frac{7}{4} x - 7 = 14 \][/tex]
3. Add 7 to both sides:
[tex]\[ \frac{7}{4} x = 14 + 7 \][/tex]
[tex]\[ \frac{7}{4} x = 21 \][/tex]
4. Multiply both sides by [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[ x = 21 \times \frac{4}{7} \][/tex]
[tex]\[ x = 3 \times 4 \][/tex]
[tex]\[ x = 12 \][/tex]
Option D does not give [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
