Certainly! Let's solve the equation step-by-step and match each step to its justification.
1. Start with the given equation:
[tex]\[
2x + 5 = 19
\][/tex]
Justification: Given
2. Subtract 5 from both sides of the equation:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
Simplifying both sides, we have:
[tex]\[
2x = 14
\][/tex]
Justification: Subtraction property of equality
3. Next, divide both sides by 2:
[tex]\[
\frac{2x}{2} = \frac{14}{2}
\][/tex]
Simplifying both sides, we have:
[tex]\[
x = 7
\][/tex]
Justification: Division property of equality
Summarizing the steps and their justifications:
1. [tex]\( 2x + 5 = 19 \)[/tex]
- Justification: Given
2. [tex]\( 2x + 5 - 5 = 19 - 5 \)[/tex]
- Justification: Subtraction property of equality
3. [tex]\( 2x = 14 \)[/tex]
- Justification: Subtract
4. [tex]\( \frac{2x}{2} = \frac{14}{2} \)[/tex]
- Justification: Division property of equality
5. [tex]\( x = 7 \)[/tex]
- Justification: Divide
By following these steps, we have solved the equation [tex]\( 2x + 5 = 19 \)[/tex] and found that [tex]\( x = 7 \)[/tex].
