Question

Translate each equation into a sentence.

$\frac{3}{4}{w}^2+\frac{2}{3}w-\frac{1}{5}=2$

Short answer

The required sentence is:

Three fourth times of the square of the number$\mathit{w}$ plus two third of the$\mathit{w}$ minus one fifth is equal to two.

Step-by-step solution

Step 1. Apply the concept of raising variable to an index.

When a variable is multiplied by itself we raise the index/exponent of the variable by two, when it is multiplied once more to this product we raise the index to three.

In this fashion variables are written, for example:

$\begin{array}{l}x\times x=x^2\\ x\times x\times x=x^3\end{array}$

Thus$w^2$is$w$raised to the second power.

Step 2. Apply the concept of multiplication of a constant and a variable.

When a constant is multiplied by a variable we just append the constant in front of the variable.

We are given the expression $\frac{3}{4}{w}^2+\frac{2}{3}w-\frac{1}{5}=2$, so first terms is being multiplied by $\frac{3}{4}$, and in the middle term, variable$w$ is being multiplied by $\frac{2}{3}$.

Step 3. Apply the concept of sum for unlike terms.

Like terms are the terms having the same variables and being raised to the same index. A coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

For example$4x$ and$5x$ are like terms.

Unlike terms are the terms not having the same variables and or are raised to a different index.

For example, 4 and$5x$ are unlike terms.

We can add like terms by adding their coefficients, we cannot add the unlike terms.

Now we are given the expression $\frac{3}{4}{w}^2+\frac{2}{3}w-\frac{1}{5}=2$, so$\frac{3}{4}{w}^2$ and$\frac{3}{4}{w}^2+\frac{2}{3}w-\frac{1}{5}=2$ is being added with $-\frac{1}{5}$.

Step 4. Evaluate the results.

Now it is given thatthe expression $\frac{3}{4}{w}^2+\frac{2}{3}w-\frac{1}{5}=2$, is equal to 2.

Thus, the required sentence is:

Three fourth times of the square of the number$w$plus two-third of the$w$minus one-fifth is equal to two.