Question

a solution method for solving the equation $2x - 3 = 5$ is shown in the table. drag properties to the table to justify the steps in the solution method. \
\

solution step	justification	\
---	---	\
$2x - 3 = 5$	given	\
$2x - 3 + 3 = 5 + 3$		\
$2x + 0 = 8$		\
$2x = 8$		\
$\frac{1}{2}(2x) = \frac{1}{2}(8)$		\
$x = 4$		\

\
properties: addition, multiplication, addition property of equality, property of multiplication, property of equality, identity property of addition, symmetric property of equality, associative property of add, identity property o, transitive property

Explanation:

Step1: Match step to equality property

The step $2x - 3 + 3 = 5 + 3$ uses the Addition Property of Equality (adding the same value to both sides of an equation preserves equality).

Step2: Match step to addition identity

The step $2x + 0 = 8$ uses the Identity Property of Addition (adding 0 to a number leaves it unchanged, since $-3+3=0$).

Step3: Match step to simplification

The step $2x = 8$ is a simplification of $2x+0=8$, which is justified by the Identity Property of Addition result (no new property, just restating the simplified form).

Step4: Match step to equality property

The step $\frac{1}{2}(2x) = \frac{1}{2}(8)$ uses the Multiplication Property of Equality (multiplying both sides of an equation by the same non-zero value preserves equality).

Step5: Match step to multiplication identity

The step $x = 4$ uses the Identity Property of Multiplication (multiplying a number by its reciprocal gives 1, since $\frac{1}{2} \times 2 = 1$, so $1 \times x = x$).

Answer:

Solution Step	Justification
$2x - 3 + 3 = 5 + 3$	Addition Property of Equality
$2x + 0 = 8$	Identity Property of Addition
$2x = 8$	Simplification (Identity Property result)
$\frac{1}{2}(2x) = \frac{1}{2}(8)$	Multiplication Property of Equality
$x = 4$	Identity Property of Multiplication