Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Let's solve each of the equations step by step.
### i) [tex]\(5x - 3 = 3x + 7\)[/tex]
1. Move the [tex]\(3x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 5x - 3 - 3x = 7 \][/tex]
2. Simplify the left side:
[tex]\[ 2x - 3 = 7 \][/tex]
3. Move the constant term [tex]\(-3\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = 7 + 3 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = 10 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{10}{2} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution is [tex]\( x = 5 \)[/tex].
### ii) [tex]\(4x + 2 = 2x - 6\)[/tex]
1. Move the [tex]\(2x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 4x + 2 - 2x = -6 \][/tex]
2. Simplify the left side:
[tex]\[ 2x + 2 = -6 \][/tex]
3. Move the constant term [tex]\(2\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = -6 - 2 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = -8 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-8}{2} \][/tex]
[tex]\[ x = -4 \][/tex]
So, the solution is [tex]\( x = -4 \)[/tex].
### iii) [tex]\(4x + 5 = 13\)[/tex]
1. Move the constant term [tex]\(5\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 4x + 5 - 5 = 13 - 5 \][/tex]
2. Simplify both sides:
[tex]\[ 4x = 8 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{8}{4} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution is [tex]\( x = 2 \)[/tex].
### Summary
The solutions for the given equations are:
i) [tex]\( x = 5 \)[/tex]
ii) [tex]\( x = -4 \)[/tex]
iii) [tex]\( x = 2 \)[/tex]
### i) [tex]\(5x - 3 = 3x + 7\)[/tex]
1. Move the [tex]\(3x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 5x - 3 - 3x = 7 \][/tex]
2. Simplify the left side:
[tex]\[ 2x - 3 = 7 \][/tex]
3. Move the constant term [tex]\(-3\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = 7 + 3 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = 10 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{10}{2} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution is [tex]\( x = 5 \)[/tex].
### ii) [tex]\(4x + 2 = 2x - 6\)[/tex]
1. Move the [tex]\(2x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 4x + 2 - 2x = -6 \][/tex]
2. Simplify the left side:
[tex]\[ 2x + 2 = -6 \][/tex]
3. Move the constant term [tex]\(2\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = -6 - 2 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = -8 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-8}{2} \][/tex]
[tex]\[ x = -4 \][/tex]
So, the solution is [tex]\( x = -4 \)[/tex].
### iii) [tex]\(4x + 5 = 13\)[/tex]
1. Move the constant term [tex]\(5\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 4x + 5 - 5 = 13 - 5 \][/tex]
2. Simplify both sides:
[tex]\[ 4x = 8 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{8}{4} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution is [tex]\( x = 2 \)[/tex].
### Summary
The solutions for the given equations are:
i) [tex]\( x = 5 \)[/tex]
ii) [tex]\( x = -4 \)[/tex]
iii) [tex]\( x = 2 \)[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.