Question

(x÷3/4)*3/5=4/5 ____________ (5/7*x)*7/5=9/10

Answer 1

Let's solve the equations step by step:

Equation 1: (x ÷ 3/4) * 3/5 = 4/5

To solve this equation, we need to simplify the expression first.

Step 1: Simplify the division operation (x ÷ 3/4) To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3.

(x ÷ 3/4) * 3/5 = x * (4/3) * 3/5

Step 2: Simplify the expression further Multiply the numerators together and the denominators together:

x * (4/3) * 3/5 = 4x/5

Now we have the simplified form of the left side of the equation.

Equation 1 becomes: 4x/5 = 4/5

Step 3: Solve for x To isolate x, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which is 5/4.

(4x/5) * (5/4) = (4/5) * (5/4)

On the left side, the 5 in the numerator and the denominator cancel out, leaving us with:

4x/4 = 4/5

Simplifying further:

x = 4/5

So the solution to equation 1 is x = 4/5.

Equation 2: (5/7 * x) * 7/5 = 9/10

Similarly, let's solve this equation step by step.

Step 1: Simplify the expression Multiplying fractions is straightforward. Multiply the numerators together and the denominators together:

(5/7 * x) * 7/5 = 35x/35

Step 2: Simplify further The numerator and denominator both have a common factor of 35. Canceling out the common factor, we get:

35x/35 = x

Equation 2 becomes: x = 9/10

So the solution to equation 2 is x = 9/10.

Therefore, the solutions to the given equations are x = 4/5 and x = 9/10, respectively.