Get comprehensive answers to your questions with the help of IDNLearn.com's community. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.
Sagot :
Sure! I'll walk through each equation step-by-step to show how to solve them.
### Equation 7: [tex]\(\frac{x-4}{3} - 5 = 0\)[/tex]
1. Start by isolating the term with [tex]\(x\)[/tex]:
[tex]\[ \frac{x-4}{3} = 5 \][/tex]
2. Multiply both sides by 3 to clear the fraction:
[tex]\[ x - 4 = 15 \][/tex]
3. Add 4 to both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = 19 \][/tex]
So, [tex]\( x = 19 \)[/tex].
### Equation 8: [tex]\( x - \frac{x+2}{12} = \frac{5x}{2} \)[/tex]
1. Start by clearing the fraction by multiplying every term by 12:
[tex]\[ 12x - (x + 2) = 6 \times 5x \][/tex]
2. Simplify the equation:
[tex]\[ 12x - x - 2 = 30x \][/tex]
[tex]\[ 11x - 2 = 30x \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 11x - 30x = 2 \][/tex]
[tex]\[ -19x = 2 \][/tex]
4. Divide by -19 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{2}{19} \][/tex]
So, [tex]\( x = -\frac{2}{19} \)[/tex].
### Equation 9: [tex]\( x - \frac{5x-1}{3} = 4x - \frac{3}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 15 (LCM of 3 and 5):
[tex]\[ 15x - 5(5x - 1) = 60x - 3 \][/tex]
2. Expand and simplify:
[tex]\[ 15x - 25x + 5 = 60x - 3 \][/tex]
[tex]\[ -10x + 5 = 60x - 3 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -10x - 60x = -3 - 5 \][/tex]
[tex]\[ -70x = -8 \][/tex]
4. Divide by -70 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-8}{-70} = \frac{8}{70} = \frac{4}{35} \approx 0.114 \][/tex]
So, [tex]\( x \approx 0.200 \)[/tex]. (Correction: It's exact [tex]\(0.200\)[/tex])
### Equation 10: [tex]\( 10x - \frac{8x - 3}{4} = 2(x - 3) \)[/tex]
1. Clear the fraction by multiplying every term by 4:
[tex]\[ 40x - (8x - 3) = 8(x - 3) \][/tex]
2. Distribute and simplify:
[tex]\[ 40x - 8x + 3 = 8x - 24 \][/tex]
[tex]\[ 32x + 3 = 8x - 24 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 32x - 8x = -24 - 3 \][/tex]
[tex]\[ 24x = -27 \][/tex]
4. Divide by 24 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{27}{24} = -\frac{9}{8} \][/tex]
So, [tex]\( x = -\frac{9}{8} \)[/tex].
### Equation 11: [tex]\(\frac{x-2}{3} - \frac{x-3}{4} = \frac{x-4}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 60 (LCM of 3, 4, and 5):
[tex]\[ 20(x - 2) - 15(x - 3) = 12(x - 4) \][/tex]
2. Distribute and simplify:
[tex]\[ 20x - 40 - 15x + 45 = 12x - 48 \][/tex]
[tex]\[ 5x + 5 = 12x - 48 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 5x - 12x = -48 - 5 \][/tex]
[tex]\[ -7x = -53 \][/tex]
4. Divide by -7 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{53}{7} \][/tex]
So, [tex]\( x = \frac{53}{7} \)[/tex].
### Equation 12: [tex]\(\frac{x-1}{2} - \frac{x-2}{3} - \frac{x-3}{4} = -\frac{x-5}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 60 (LCM of 2, 3, 4, and 5):
[tex]\[ 30(x - 1) - 20(x - 2) - 15(x - 3) = -12(x - 5) \][/tex]
2. Distribute and simplify:
[tex]\[ 30x - 30 - 20x + 40 - 15x + 45 = -12x + 60 \][/tex]
[tex]\[ (30x - 20x - 15x) = (-12x + 60 + 30 - 40 - 45) \][/tex]
[tex]\[ -5x - 30 + 40 + 45 = -12x + 60 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -5x + 12x = -30 + 40 + 45 - 60 \][/tex]
[tex]\[ 7x = 5 \][/tex]
4. Divide by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{5}{7} \][/tex]
So, [tex]\( x = \frac{5}{7} \)[/tex].
### Equation 13: [tex]\( x - (5x - 1) - \frac{7 - 5x}{10} = 1 \)[/tex]
1. Clear the fraction by multiplying every term by 10:
[tex]\[ 10x - 10(5x - 1) - (7 - 5x) = 10 \][/tex]
2. Distribute and simplify:
[tex]\[ 10x - 50x + 10 - 7 + 5x = 10 \][/tex]
[tex]\[ (10x - 50x + 5x) + 10 - 7 = 10 \][/tex]
[tex]\[ -35x + 10 -7 = 10 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -35x + 3 = 10 \][/tex]
[tex]\[ -35x = 7 \][/tex]
4. Divide by -35 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{7}{35} = -\frac{1}{5} \][/tex]
So, [tex]\( x = -\frac{1}{5} \)[/tex].
### Equation 14: [tex]\( 2x - \frac{5x - 6}{4} + \frac{1}{3}(x - 5) = -5x \)[/tex]
1. Clear the fraction by multiplying every term by 12 (LCM of 4 and 3):
[tex]\[ 24x - 3(5x - 6) + 4(x - 5) = -60x \][/tex]
2. Distribute and simplify:
[tex]\[ 24x - 15x + 18 + 4x - 20 = -60x \][/tex]
[tex]\[ (24x - 15x + 4x) + (18 - 20) = -60x \][/tex]
[tex]\[ 13x - 2 = -60x \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 13x + 60x = 2 \][/tex]
[tex]\[ 73x = 73 \][/tex]
4. Divide by 73 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{2}{73} \][/tex]
So, [tex]\( x = \approx 0.0273972602739726 \)[/tex] (Exact: not fraction)
### Equation 15: [tex]\( 4 - \frac{10x + 1}{6} = 4x - \frac{16x + 3}{4} \)[/tex]
1. Clear the fraction by multiplying every term by 12 (LCM of 6 and 4):
[tex]\[ 48 - 2(10x + 1) = 12 * 4x - 3(16x + 3) \][/tex]
2. Distribute and simplify:
[tex]\[ 48 - 20x - 2 = 48x - 48x - 9 \][/tex]
[tex]\[ 46 - 20x = 48x - 9 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 46 = 48x - 9 + 20x \][/tex]
[tex]\[ 75= 48x + 20 x = 53 \][/tex]
\]
4. Divide by 4 to solve for [tex]\(x\)[/tex]:
\[
x = \frac{11}{4} = develop exact . calculation
]
So, \( x = 11/4).
### Equation 7: [tex]\(\frac{x-4}{3} - 5 = 0\)[/tex]
1. Start by isolating the term with [tex]\(x\)[/tex]:
[tex]\[ \frac{x-4}{3} = 5 \][/tex]
2. Multiply both sides by 3 to clear the fraction:
[tex]\[ x - 4 = 15 \][/tex]
3. Add 4 to both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = 19 \][/tex]
So, [tex]\( x = 19 \)[/tex].
### Equation 8: [tex]\( x - \frac{x+2}{12} = \frac{5x}{2} \)[/tex]
1. Start by clearing the fraction by multiplying every term by 12:
[tex]\[ 12x - (x + 2) = 6 \times 5x \][/tex]
2. Simplify the equation:
[tex]\[ 12x - x - 2 = 30x \][/tex]
[tex]\[ 11x - 2 = 30x \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 11x - 30x = 2 \][/tex]
[tex]\[ -19x = 2 \][/tex]
4. Divide by -19 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{2}{19} \][/tex]
So, [tex]\( x = -\frac{2}{19} \)[/tex].
### Equation 9: [tex]\( x - \frac{5x-1}{3} = 4x - \frac{3}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 15 (LCM of 3 and 5):
[tex]\[ 15x - 5(5x - 1) = 60x - 3 \][/tex]
2. Expand and simplify:
[tex]\[ 15x - 25x + 5 = 60x - 3 \][/tex]
[tex]\[ -10x + 5 = 60x - 3 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -10x - 60x = -3 - 5 \][/tex]
[tex]\[ -70x = -8 \][/tex]
4. Divide by -70 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-8}{-70} = \frac{8}{70} = \frac{4}{35} \approx 0.114 \][/tex]
So, [tex]\( x \approx 0.200 \)[/tex]. (Correction: It's exact [tex]\(0.200\)[/tex])
### Equation 10: [tex]\( 10x - \frac{8x - 3}{4} = 2(x - 3) \)[/tex]
1. Clear the fraction by multiplying every term by 4:
[tex]\[ 40x - (8x - 3) = 8(x - 3) \][/tex]
2. Distribute and simplify:
[tex]\[ 40x - 8x + 3 = 8x - 24 \][/tex]
[tex]\[ 32x + 3 = 8x - 24 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 32x - 8x = -24 - 3 \][/tex]
[tex]\[ 24x = -27 \][/tex]
4. Divide by 24 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{27}{24} = -\frac{9}{8} \][/tex]
So, [tex]\( x = -\frac{9}{8} \)[/tex].
### Equation 11: [tex]\(\frac{x-2}{3} - \frac{x-3}{4} = \frac{x-4}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 60 (LCM of 3, 4, and 5):
[tex]\[ 20(x - 2) - 15(x - 3) = 12(x - 4) \][/tex]
2. Distribute and simplify:
[tex]\[ 20x - 40 - 15x + 45 = 12x - 48 \][/tex]
[tex]\[ 5x + 5 = 12x - 48 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 5x - 12x = -48 - 5 \][/tex]
[tex]\[ -7x = -53 \][/tex]
4. Divide by -7 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{53}{7} \][/tex]
So, [tex]\( x = \frac{53}{7} \)[/tex].
### Equation 12: [tex]\(\frac{x-1}{2} - \frac{x-2}{3} - \frac{x-3}{4} = -\frac{x-5}{5} \)[/tex]
1. Clear the fractions by multiplying every term by 60 (LCM of 2, 3, 4, and 5):
[tex]\[ 30(x - 1) - 20(x - 2) - 15(x - 3) = -12(x - 5) \][/tex]
2. Distribute and simplify:
[tex]\[ 30x - 30 - 20x + 40 - 15x + 45 = -12x + 60 \][/tex]
[tex]\[ (30x - 20x - 15x) = (-12x + 60 + 30 - 40 - 45) \][/tex]
[tex]\[ -5x - 30 + 40 + 45 = -12x + 60 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -5x + 12x = -30 + 40 + 45 - 60 \][/tex]
[tex]\[ 7x = 5 \][/tex]
4. Divide by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{5}{7} \][/tex]
So, [tex]\( x = \frac{5}{7} \)[/tex].
### Equation 13: [tex]\( x - (5x - 1) - \frac{7 - 5x}{10} = 1 \)[/tex]
1. Clear the fraction by multiplying every term by 10:
[tex]\[ 10x - 10(5x - 1) - (7 - 5x) = 10 \][/tex]
2. Distribute and simplify:
[tex]\[ 10x - 50x + 10 - 7 + 5x = 10 \][/tex]
[tex]\[ (10x - 50x + 5x) + 10 - 7 = 10 \][/tex]
[tex]\[ -35x + 10 -7 = 10 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ -35x + 3 = 10 \][/tex]
[tex]\[ -35x = 7 \][/tex]
4. Divide by -35 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{7}{35} = -\frac{1}{5} \][/tex]
So, [tex]\( x = -\frac{1}{5} \)[/tex].
### Equation 14: [tex]\( 2x - \frac{5x - 6}{4} + \frac{1}{3}(x - 5) = -5x \)[/tex]
1. Clear the fraction by multiplying every term by 12 (LCM of 4 and 3):
[tex]\[ 24x - 3(5x - 6) + 4(x - 5) = -60x \][/tex]
2. Distribute and simplify:
[tex]\[ 24x - 15x + 18 + 4x - 20 = -60x \][/tex]
[tex]\[ (24x - 15x + 4x) + (18 - 20) = -60x \][/tex]
[tex]\[ 13x - 2 = -60x \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 13x + 60x = 2 \][/tex]
[tex]\[ 73x = 73 \][/tex]
4. Divide by 73 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{2}{73} \][/tex]
So, [tex]\( x = \approx 0.0273972602739726 \)[/tex] (Exact: not fraction)
### Equation 15: [tex]\( 4 - \frac{10x + 1}{6} = 4x - \frac{16x + 3}{4} \)[/tex]
1. Clear the fraction by multiplying every term by 12 (LCM of 6 and 4):
[tex]\[ 48 - 2(10x + 1) = 12 * 4x - 3(16x + 3) \][/tex]
2. Distribute and simplify:
[tex]\[ 48 - 20x - 2 = 48x - 48x - 9 \][/tex]
[tex]\[ 46 - 20x = 48x - 9 \][/tex]
3. Get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 46 = 48x - 9 + 20x \][/tex]
[tex]\[ 75= 48x + 20 x = 53 \][/tex]
\]
4. Divide by 4 to solve for [tex]\(x\)[/tex]:
\[
x = \frac{11}{4} = develop exact . calculation
]
So, \( x = 11/4).
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.
