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What is the justification for step 1 in the solution process?
[tex]\[ 8x + 15 = 11x + 2 \][/tex]

Step 1: [tex]\[ 8x = 11x - 13 \][/tex]

A. the addition property of equality
B. the subtraction property of equality
C. the division property of equality
D. the multiplication property of equality

Sagot :

GinnyAnsweridn
To determine which property justifies step 1 in solving the equation:
[tex]$ 8x + 15 = 11x + 2 $[/tex]

Step 1 given is:
[tex]$ 8x = 11x - 13 $[/tex]

Let’s analyze how we go from the initial equation to this step.

The initial equation is:
[tex]$ 8x + 15 = 11x + 2 $[/tex]

We subtract [tex]\(2\)[/tex] from both sides:
[tex]$ 8x + 15 - 2 = 11x $[/tex]

This simplifies to:
[tex]$ 8x + 13 = 11x $[/tex]

Then, we subtract [tex]\(8x\)[/tex] from both sides:
[tex]$ 13 = 3x $[/tex]

This can be rewritten as:
[tex]$ 8x = 11x - 13 $[/tex]

So, we have used subtraction to isolate terms involving [tex]\(x\)[/tex]. Specifically, we subtracted [tex]\(8x\)[/tex] from both sides of the equation:
[tex]$ 8x + 15 - 8x = 11x + 2 - 8x $[/tex]

The subtraction of [tex]\(8x\)[/tex] from both sides leads us to:
[tex]$ 15 = 3x + 2 $[/tex]

Which can then be rewritten to focus on isolating [tex]\(x\)[/tex]:
[tex]$ 8x = 11x - 13 $[/tex]

Thus, the property of equality used to justify step 1 is:

B. the subtraction property of equality
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