IDNLearn.com: Your destination for reliable and timely answers to any question. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
Sure, let's solve each equation one by one and check the results.
### 1. Solve [tex]\( 3x = 2x + 18 \)[/tex]
First, let's isolate [tex]\( x \)[/tex]:
[tex]\[ 3x - 2x = 18 \][/tex]
[tex]\[ x = 18 \][/tex]
The solution for this equation is [tex]\( x = 18 \)[/tex].
### 2. Solve [tex]\( 5t - 3 = 3t - 5 \)[/tex]
First, let's get all the [tex]\( t \)[/tex] terms on one side:
[tex]\[ 5t - 3t = -5 + 3 \][/tex]
[tex]\[ 2t = -2 \][/tex]
Now, divide both sides by 2:
[tex]\[ t = -1 \][/tex]
The solution for this equation is [tex]\( t = -1 \)[/tex].
### 3. Solve [tex]\( 4z + 3 = 6 + 2z \)[/tex]
First, let's get all the [tex]\( z \)[/tex] terms on one side:
[tex]\[ 4z - 2z = 6 - 3 \][/tex]
[tex]\[ 2z = 3 \][/tex]
Now, divide both sides by 2:
[tex]\[ z = \frac{3}{2} \][/tex]
The solution for this equation is [tex]\( z = \frac{3}{2} \)[/tex].
### 4. Solve [tex]\( 2x - 1 = 14 - x \)[/tex]
First, let's get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[ 2x + x = 14 + 1 \][/tex]
[tex]\[ 3x = 15 \][/tex]
Now, divide both sides by 3:
[tex]\[ x = 5 \][/tex]
The solution for this equation is [tex]\( x = 5 \)[/tex].
### 5. Solve [tex]\( x = \frac{4}{5}(x + 10) \)[/tex]
First, let's distribute the [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[ x = \frac{4}{5}x + 8 \][/tex]
Now, let's get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[ x - \frac{4}{5}x = 8 \][/tex]
[tex]\[ \frac{1}{5}x = 8 \][/tex]
Finally, multiply both sides by 5:
[tex]\[ x = 40 \][/tex]
The solution for this equation is [tex]\( x = 40 \)[/tex].
### 6. Solve [tex]\( \frac{2x}{3} + 1 = \frac{7x}{15} + 3 \)[/tex]
First, get all the [tex]\( x \)[/tex] terms together:
[tex]\[ \frac{2x}{3} - \frac{7x}{15} = 3 - 1 \][/tex]
To combine the [tex]\( x \)[/tex] terms, we need a common denominator:
[tex]\[ \frac{10x}{15} - \frac{7x}{15} = 2 \][/tex]
[tex]\[ \frac{3x}{15} = 2 \][/tex]
[tex]\[ \frac{x}{5} = 2 \][/tex]
Finally, multiply both sides by 5:
[tex]\[ x = 10 \][/tex]
The solution for this equation is [tex]\( x = 10 \)[/tex].
### 7. Solve [tex]\( 3m = 5m - \frac{8}{5} \)[/tex]
First, get all the [tex]\( m \)[/tex] terms together:
[tex]\[ 3m - 5m = -\frac{8}{5} \][/tex]
[tex]\[ -2m = -\frac{8}{5} \][/tex]
Now, divide both sides by [tex]\(-2\)[/tex]:
[tex]\[ m = \frac{8}{10} \][/tex]
[tex]\[ m = 0.8 \][/tex]
The solution for this equation is [tex]\( m = 0.8 \)[/tex].
So the solutions are:
1. [tex]\( x = 18 \)[/tex]
2. [tex]\( t = -1 \)[/tex]
3. [tex]\( z = \frac{3}{2} \)[/tex]
4. [tex]\( x = 5 \)[/tex]
5. [tex]\( x = 40 \)[/tex]
6. [tex]\( x = 10 \)[/tex]
7. [tex]\( m = 0.8 \)[/tex]
### 1. Solve [tex]\( 3x = 2x + 18 \)[/tex]
First, let's isolate [tex]\( x \)[/tex]:
[tex]\[ 3x - 2x = 18 \][/tex]
[tex]\[ x = 18 \][/tex]
The solution for this equation is [tex]\( x = 18 \)[/tex].
### 2. Solve [tex]\( 5t - 3 = 3t - 5 \)[/tex]
First, let's get all the [tex]\( t \)[/tex] terms on one side:
[tex]\[ 5t - 3t = -5 + 3 \][/tex]
[tex]\[ 2t = -2 \][/tex]
Now, divide both sides by 2:
[tex]\[ t = -1 \][/tex]
The solution for this equation is [tex]\( t = -1 \)[/tex].
### 3. Solve [tex]\( 4z + 3 = 6 + 2z \)[/tex]
First, let's get all the [tex]\( z \)[/tex] terms on one side:
[tex]\[ 4z - 2z = 6 - 3 \][/tex]
[tex]\[ 2z = 3 \][/tex]
Now, divide both sides by 2:
[tex]\[ z = \frac{3}{2} \][/tex]
The solution for this equation is [tex]\( z = \frac{3}{2} \)[/tex].
### 4. Solve [tex]\( 2x - 1 = 14 - x \)[/tex]
First, let's get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[ 2x + x = 14 + 1 \][/tex]
[tex]\[ 3x = 15 \][/tex]
Now, divide both sides by 3:
[tex]\[ x = 5 \][/tex]
The solution for this equation is [tex]\( x = 5 \)[/tex].
### 5. Solve [tex]\( x = \frac{4}{5}(x + 10) \)[/tex]
First, let's distribute the [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[ x = \frac{4}{5}x + 8 \][/tex]
Now, let's get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[ x - \frac{4}{5}x = 8 \][/tex]
[tex]\[ \frac{1}{5}x = 8 \][/tex]
Finally, multiply both sides by 5:
[tex]\[ x = 40 \][/tex]
The solution for this equation is [tex]\( x = 40 \)[/tex].
### 6. Solve [tex]\( \frac{2x}{3} + 1 = \frac{7x}{15} + 3 \)[/tex]
First, get all the [tex]\( x \)[/tex] terms together:
[tex]\[ \frac{2x}{3} - \frac{7x}{15} = 3 - 1 \][/tex]
To combine the [tex]\( x \)[/tex] terms, we need a common denominator:
[tex]\[ \frac{10x}{15} - \frac{7x}{15} = 2 \][/tex]
[tex]\[ \frac{3x}{15} = 2 \][/tex]
[tex]\[ \frac{x}{5} = 2 \][/tex]
Finally, multiply both sides by 5:
[tex]\[ x = 10 \][/tex]
The solution for this equation is [tex]\( x = 10 \)[/tex].
### 7. Solve [tex]\( 3m = 5m - \frac{8}{5} \)[/tex]
First, get all the [tex]\( m \)[/tex] terms together:
[tex]\[ 3m - 5m = -\frac{8}{5} \][/tex]
[tex]\[ -2m = -\frac{8}{5} \][/tex]
Now, divide both sides by [tex]\(-2\)[/tex]:
[tex]\[ m = \frac{8}{10} \][/tex]
[tex]\[ m = 0.8 \][/tex]
The solution for this equation is [tex]\( m = 0.8 \)[/tex].
So the solutions are:
1. [tex]\( x = 18 \)[/tex]
2. [tex]\( t = -1 \)[/tex]
3. [tex]\( z = \frac{3}{2} \)[/tex]
4. [tex]\( x = 5 \)[/tex]
5. [tex]\( x = 40 \)[/tex]
6. [tex]\( x = 10 \)[/tex]
7. [tex]\( m = 0.8 \)[/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.
