Let's solve the equation [tex]\(2x + 5 = 19\)[/tex] step-by-step and match each step to its justification:
1. Given:
[tex]\[
2x + 5 = 19
\][/tex]
This is the initial equation provided.
2. Subtraction Property of Equality:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
Here, we subtract 5 from both sides of the equation to isolate the term with the variable [tex]\(x\)[/tex] on one side.
3. Simplify:
[tex]\[
2x = 14
\][/tex]
After subtraction, we simplify both sides of the equation to get [tex]\(2x\)[/tex] on the left and 14 on the right.
4. Division Property of Equality:
[tex]\[
\frac{2x}{2} = \frac{14}{2}
\][/tex]
Next, we divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex].
5. Simplify:
[tex]\[
x = 7
\][/tex]
Finally, simplifying the division, we find that [tex]\(x = 7\)[/tex].
Matching each step with its justification:
- Given:
[tex]\[
2x + 5 = 19
\][/tex]
- Subtraction Property of Equality:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
(Justification: subtract)
- Simplify:
[tex]\[
2x = 14
\][/tex]
(Justification: simplification after subtraction)
- Division Property of Equality:
[tex]\[
\frac{2x}{2} = \frac{14}{2}
\][/tex]
(Justification: divide)
- Simplify:
[tex]\[
x = 7
\][/tex]
(Justification: simplification after division)
