Question

Name the properties used to solve this equation:
4/3(3/4x)=4/3 * 1/4. Given
(4/3 * 3/4)x=4/3 * 1/4 a.
1x=4/3 * 1/4. b.
x=4/3 * 1/4 c.
x=1/3 4/3*1/4=1/3

Answer 1

We want to see the properties used to solve the given equation.

The properties used are:

• Existence of the multiplicative inverse.
• Associative property of the multiplication.

Let's write step by step and see which property we used on each step.

We start with:

$\frac{4}{3} *(\frac{3}{4} *x) = \frac{4}{3} *\frac{1}{4}$

Now we use the associative property of the multiplication (says that we can multiply in any order we want) we rewrite this to:

$(\frac{4}{3} *\frac{3}{4} )*x = \frac{4}{3} *\frac{1}{4}$

Now we use the existence of the multiplicative inverse, this says that for a number a, there exist a number b such that:

a*b = 1

And we have that b = 1/a.

Then we apply that to the first factor to get:

$(\frac{4}{3} *\frac{3}{4}) *x = \frac{4}{3} *\frac{1}{4} \\\\x = \frac{4}{3} *\frac{1}{4}$

Again, using the same but with the numerator of the first factor of the right side and the denominator of the second factor of the right side we get:

$x = \frac{4}{4} *\frac{1}{3} = \frac{1}{3}$

Then the properties used are:

• Existence of the multiplicative inverse.
• Associative property of the multiplication.

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https://brainly.com/question/325258