### Question 1a
Given inequality: [tex]\(7x - 13 < 2x\)[/tex]
To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the inequality.
Let's start by subtracting [tex]\(2x\)[/tex] from both sides to combine like terms:
[tex]\[ 7x - 13 - 2x < 2x - 2x \][/tex]
[tex]\[ 5x - 13 < 0 \][/tex]
Next, we add 13 to both sides to isolate [tex]\(5x\)[/tex]:
[tex]\[ 5x - 13 + 13 < 0 + 13 \][/tex]
[tex]\[ 5x < 13 \][/tex]
Now, we'll divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[ x < \frac{13}{5} \][/tex]
[tex]\[ x < 2.6 \][/tex]
Since [tex]\(x\)[/tex] is specified to be an integer, the greatest integer values less than 2.6 are 2, 1, and 0.
Therefore, the three greatest values of [tex]\(x\)[/tex] that satisfy the inequality are:
[tex]\[ x = 2, 1, 0 \][/tex]
### Question 1b
Given inequality: [tex]\(2(x - 3) > 3(2 - x)\)[/tex]
To solve this inequality, start by distributing the constants on both sides:
[tex]\[ 2x - 6 > 6 - 3x \][/tex]
Next, combine like terms by adding [tex]\(3x\)[/tex] to both sides:
[tex]\[ 2x - 6 + 3x > 6 - 3x + 3x \][/tex]
[tex]\[ 5x - 6 > 6 \][/tex]
Then, add 6 to both sides to isolate [tex]\(5x\)[/tex]:
[tex]\[ 5x - 6 + 6 > 6 + 6 \][/tex]
[tex]\[ 5x > 12 \][/tex]
Lastly, divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[ x > \frac{12}{5} \][/tex]
[tex]\[ x > 2.4 \][/tex]
Thus, the solution to the inequality is:
[tex]\[ x > 2.4 \][/tex]
