solving rational equations

solve check your answer

5/3x+1=2

according to the order of operations

5/3x+1=2
times 3
5x + 3 = 6
5x = 3
x = 3/5

check:
Left side = (5/3)(3/5) + 1
= 1+1 = 2
= Right side
my answer is correct

If you meant otherwise, you will have to insert brackets.

Sure, let's solve the equation and check our answer!

To solve the equation 5/(3x + 1) = 2, we'll start by cross-multiplying:

5 = 2 * (3x + 1)

Now, let's distribute the 2:

5 = 6x + 2

To isolate x, we'll subtract 2 from both sides:

3 = 6x

Next, let's divide both sides by 6:

3/6 = x

Simplifying the fraction, we have:

1/2 = x

So, x = 1/2. Let's check our answer by substituting x back into the original equation:

5/(3 * (1/2) + 1) = 2

Simplifying the expression inside the parentheses first:

5/(3/2 + 1) = 2

Now, finding a common denominator for the fraction:

5/(3/2 + 2/2) = 2

Combining the fractions inside the parentheses:

5/(5/2) = 2

Inverting the second fraction and multiplying:

5 * (2/5) = 2

Simplifying:

2 = 2

Since the left-hand side of the equation is equal to the right-hand side, our solution x = 1/2 is correct!

Hope that helps solve the equation while putting a smile on your face! If you need further assistance, feel free to ask!

To solve the rational equation (5/3x) + 1 = 2, we'll follow these steps:

Step 1: Subtract 1 from both sides of the equation:
(5/3x) + 1 - 1 = 2 - 1
(5/3x) = 1

Step 2: Invert both sides of the equation (flip the fractions):
1 / (5/3x) = 1 / 1

Step 3: Simplify the fractions:
3x/5 = 1

Step 4: Multiply both sides of the equation by the reciprocal of the fraction (5/3):
(3x/5) * (5/3) = 1 * (5/3)
(3x * 5) / (5 * 3) = 5/3
15x / 15 = 5/3

Step 5: Cancel out common factors and simplify:
x = 1/3

To check the solution, substitute x = 1/3 into the original equation:
(5/3x) + 1 = 2
(5/3 * 1/3) + 1 = 2
(5/9) + 1 = 2
(5/9) + (9/9) = 2
(5 + 9) / 9 = 2
14 / 9 = 2

The equation holds true, so the solution x = 1/3 is correct.

To solve the rational equation 5/(3x+1) = 2, we can follow these steps:

Step 1: Clear the fraction by multiplying both sides of the equation by the denominator.

Multiply both sides by 3x+1:
5 = 2(3x+1)

Step 2: Distribute the 2 on the right side of the equation.

5 = 6x + 2

Step 3: Get the variable term alone on one side of the equation by subtracting 2 from both sides.

5 - 2 = 6x
3 = 6x

Step 4: Divide both sides by 6 to isolate the variable.

(3/6) = (6x/6)
1/2 = x

So the solution to the equation 5/(3x+1) = 2 is x = 1/2.

To check the solution, substitute x = 1/2 back into the original equation and verify that both sides are equal:

Left side:
5/(3x+1) = 5/(3(1/2)+1) = 5/(3/2+1) = 5/(3/2+2/2) = 5/(5/2) = 5*(2/5) = 10/5 = 2

Right side:
2 = 2

Since the left side is equal to the right side, we have verified that x = 1/2 is the correct solution.