Sure! Let's go through the solution to the equation [tex]\(2x + 5 = 19\)[/tex] 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 to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
- Justification: subtraction property of equality
3. Simplify the equation after subtraction:
[tex]\[
2x = 14
\][/tex]
- Justification: subtract
4. Divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
2x / 2 = 14 / 2
\][/tex]
- Justification: division property of equality
5. Simplify the equation after division to find the value of [tex]\(x\)[/tex]:
[tex]\[
x = 7
\][/tex]
- Justification: divide
Matching each step with its justification, we get the following pairs:
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]\(2x / 2 = 14 / 2\)[/tex] - Justification: division property of equality
5. [tex]\(x = 7\)[/tex] - Justification: divide
