Question

Which set of expressions are not equivalent?(4 1\2 a + 2) + 3 and 5 + 4 a18 a + 14 and 6 a + 12 + 2 + 1 2a0.5 a + 3.5 + 4 a and 3.5 + 4.5 a3 a + 7 +2 a and 7 a + 5

Answer 1

Solution:

Solution:

To find which of given expressions are equivalent

For the first expressions

$(4\frac{1}{2}a+2)+3\text{ and 5}+4\frac{1}{2}a$

Solving the expression

$\begin{gathered} 4\frac{1}{2}a+2+3=5+4\frac{1}{2}a \\ 5+4\frac{1}{2}a=5+4\frac{1}{2}a \end{gathered}$

The expressions are equivalent

For the second expression

$18a+14\text{ and 6a}+12+2+12a$

Solving the expression

$\begin{gathered} 18a+14=6a+12a+12+2 \\ 18a+14=18a+14 \end{gathered}$

The expressions are equivalent

For the third expression

$0.5a+3.5+4a\text{ and 3.5}+4.5a$

Solving the expression

$\begin{gathered} 3.5+0.5a+4a=3.5+4.5a \\ 3.5+4.5a=3.5+4.5a \end{gathered}$

The expressions are equivalent

For the fourth expression

$3a+7+2a\text{ and 7a}+5$

Solving the expression

$\begin{gathered} 3a+2a+7=7a+5 \\ 5a+7\ne7a+5 \end{gathered}$

The expressions are not equivalent.

Hence, the set of expressions that are not equivalent is

$3a+7+2a\text{ and 7a}+5$