1. x-9/5=1/5
2. 1/2+x=2/3
3. 1/2+x=2/3
4. x/4=3/8
5. 3/2+x=2
1.
x-9/5=1/5
x = 9/5 + 1/5
x = 10/5
x = 2
2.
1/2+x=2/3
x = 4/6 - 3/6
x = 1/6
I'll be glad to check your answers to the other three problems.
How did you get the 4/6-3/6
When we add or subtract fractions, they must have the same denominator.
2/3 = 4/6
To solve each of these equations, we will follow a step-by-step process. Let's go through each equation one by one:
1. x - 9/5 = 1/5:
- To isolate x, we need to get rid of the constant term (-9/5) on the left side. We can do this by adding 9/5 to both sides:
x - 9/5 + 9/5 = 1/5 + 9/5
x = 10/5
- Simplifying x gives us the final answer: x = 2.
2. 1/2 + x = 2/3:
- We need to isolate x by eliminating the constant term (1/2) on the left side. We can do this by subtracting 1/2 from both sides:
1/2 + x - 1/2 = 2/3 - 1/2
x = 2/3 - 1/2
- In order to subtract these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 2 is 6, so we'll convert both fractions to have a denominator of 6:
x = 4/6 - 3/6
- Now we can subtract the fractions:
x = 1/6
- The final answer is x = 1/6.
3. 1/2 + x = 2/3:
- Oops! It seems like this equation is the same as the previous one. Therefore, the solution is also x = 1/6.
4. x/4 = 3/8:
- To get rid of the fraction on the left side, we can multiply both sides by the reciprocal of 4, which is 8/4 (or simply 2):
(x/4) * (8/4) = (3/8) * (8/4)
x * 2/4 = 3/8
- Now we can simplify the left side:
(2x/4) = 3/8
x/2 = 3/8
- To further isolate x, we can multiply both sides by 2:
(x/2) * 2 = (3/8) * 2
x = 6/8
- Simplifying x gives us the final answer: x = 3/4.
5. 3/2 + x = 2:
- We need to isolate x by eliminating the constant term (3/2) on the left side. We'll do this by subtracting 3/2 from both sides:
3/2 + x - 3/2 = 2 - 3/2
x = 2 - 3/2
- In order to subtract 3/2 from 2, we need a common denominator. The least common multiple (LCM) of 2 and 2 is 2, so we'll convert both numbers to have a denominator of 2:
x = 4/2 - 3/2
- Now we can subtract the fractions:
x = 1/2
- The final answer is x = 1/2.
Remember, when solving equations, the goal is to isolate the variable on one side of the equation. You can achieve this by performing the same operations on both sides of the equation, ensuring to simplify along the way.