Answer :
To determine whether the inequality [tex]\(6x - 4 \leq 3x - 4\)[/tex] holds true for [tex]\(x = 2\)[/tex], we can follow these steps:
1. Substitute [tex]\(x = 2\)[/tex] into the inequality:
- Start with the original inequality: [tex]\(6x - 4 \leq 3x - 4\)[/tex].
- Substitute [tex]\(x = 2\)[/tex] into both sides of the inequality.
2. Calculate the left side of the inequality:
[tex]\[ \text{Left side} = 6(2) - 4 = 12 - 4 = 8 \][/tex]
3. Calculate the right side of the inequality:
[tex]\[ \text{Right side} = 3(2) - 4 = 6 - 4 = 2 \][/tex]
4. Compare the results:
- The left side evaluates to 8.
- The right side evaluates to 2.
- Therefore, the inequality is [tex]\(8 \leq 2\)[/tex].
5. Check the inequality:
- The statement [tex]\(8 \leq 2\)[/tex] is false.
Hence, when [tex]\(x = 2\)[/tex], the inequality [tex]\(6x - 4 \leq 3x - 4\)[/tex] does not hold true.
1. Substitute [tex]\(x = 2\)[/tex] into the inequality:
- Start with the original inequality: [tex]\(6x - 4 \leq 3x - 4\)[/tex].
- Substitute [tex]\(x = 2\)[/tex] into both sides of the inequality.
2. Calculate the left side of the inequality:
[tex]\[ \text{Left side} = 6(2) - 4 = 12 - 4 = 8 \][/tex]
3. Calculate the right side of the inequality:
[tex]\[ \text{Right side} = 3(2) - 4 = 6 - 4 = 2 \][/tex]
4. Compare the results:
- The left side evaluates to 8.
- The right side evaluates to 2.
- Therefore, the inequality is [tex]\(8 \leq 2\)[/tex].
5. Check the inequality:
- The statement [tex]\(8 \leq 2\)[/tex] is false.
Hence, when [tex]\(x = 2\)[/tex], the inequality [tex]\(6x - 4 \leq 3x - 4\)[/tex] does not hold true.
