Question

Determine whether the expressions are equivalent. Explain your reasoning.

Expression 1	$1.25x+4+0.75x-3$
Expression 2	$2x+1$

Answer 1

Step 1: Simplify both the expressions to the simplest form:-
Expression $1$:- $1.25x+4+0.75x-3$
$=1.25x+4+0.75x-3$
$=(1.25+0.75)x+4-3$
$=2x+1$ (simplest form )
Expression $2$ :- $2x+1$
$=2x+1$ (simplest form)
Step 2: Comparing both the expressions:-

Now comparing both the expression we can see that expression $1$ is equivalent to expression $2$.

Because the coefficient of the variable $x$ in both the expression is same in its simplest form and also the constant term is same in its simplest form.
Hence, $\left(1.25x+4+0.75x-3\right)$ and $\left(2x+1\right)$ are equivalent.