Question

1. write an expression that is equivalent to 2.5x + (-5y) - 2.5.
2. co

exp
8.
b

1. which shows an expression equivalent to 6x + 8.25 - 4.5x?

a 1.5x - 8.25
b 10.5x + 8.25
c 1.5x + 8.25
d 10.5x - 8.25
assessment practice

1. select all expressions equivalent to $-\frac{2}{3}x + 2$.

$ -2 - \frac{2}{3}x $
$ 2 - \frac{2}{3}x $
$ -1 - \frac{2}{3}x + 1 $
$ -\frac{1}{3}x - 4 + 2 $
$ -\frac{2}{3}x - 3 + 5 $

Explanation:

Question 9

Step1: Simplify the expression

The original expression is \(2.5x + (-5y) - 2.5\). We can rewrite \(+(-5y)\) as \(-5y\). So the equivalent expression is \(2.5x - 5y - 2.5\).

Step1: Combine like terms

We have the expression \(6x + 8.25 - 4.5x\). Combine the \(x\)-terms: \(6x - 4.5x = 1.5x\).

Step2: Write the simplified expression

The constant term \(8.25\) remains as it is. So the simplified expression is \(1.5x + 8.25\).

We need to check each option to see if it is equivalent to \(-\frac{2}{3}x + 2\).

1. For \(-2 - \frac{2}{3}x\): The constant term is \(-2\), which is not equal to \(2\) in the original expression. So this is not equivalent.
2. For \(2 - \frac{2}{3}x\): Rearranging, we get \(-\frac{2}{3}x + 2\), which is the same as the original expression. So this is equivalent.
3. For \(-1 - \frac{2}{3}x + 3\): Combine the constant terms: \(-1 + 3 = 2\). So the expression becomes \(-\frac{2}{3}x + 2\), which is equivalent.
4. For \(-\frac{1}{3}x - 4 + 2\): Combine the constant terms: \(-4 + 2 = -2\), and the \(x\)-term is \(-\frac{1}{3}x\), which is not the same as \(-\frac{2}{3}x\) in the original expression. So this is not equivalent.
5. For \(-\frac{2}{3}x - 3 + 5\): Combine the constant terms: \(-3 + 5 = 2\). So the expression becomes \(-\frac{2}{3}x + 2\), which is equivalent.

Answer:

\(2.5x - 5y - 2.5\)

Question 11