QuestionSolve the equation $6 x - 9 = 45$ and justify each step using properties of equality.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $6x -9 =45$ . . We are to justify each step in the solution of this equation.
3. We have the following properties at our disposal addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality, and simplification.

STEP 2

The first step is given as $6x -9 =45$ . The reason for this is that it is the given equation we are to solve.
$6x -9 =45 \quad \text{(Given)}$

STEP 3

The second step is $6x -9 +9 =45 +9$ . The reason for this is the addition property of equality, which states that if you add the same number to both sides of an equation, the equation remains true.
$6x -9 +9 =45 +9 \quad \text{(Addition property of equality)}$

STEP 4

The third step is $6x =54$ . The reason for this is simplification, which involves performing the addition operation on both sides of the equation.
$6x =54 \quad \text{(implification)}$

STEP 5

The fourth step is $\frac{x}{} = \frac{54}{}$ . The reason for this is the division property of equality, which states that if you divide both sides of an equation by the same nonzero number, the equation remains true.
$\frac{x}{} = \frac{54}{} \quad \text{(Division property of equality)}$

STEP 6

The final step is $x =9$ . The reason for this is simplification, which involves performing the division operation on both sides of the equation.
$x =9 \quad \text{(implification)}$

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