Let's simplify each given expression step-by-step.
### a) [tex]\(|+2| + |+2|\)[/tex]
1. [tex]\(|+2|\)[/tex] represents the absolute value of [tex]\(+2\)[/tex].
2. The absolute value of [tex]\(+2\)[/tex] is [tex]\(2\)[/tex].
3. Therefore, [tex]\(|+2| + |+2| = 2 + 2 = 4\)[/tex].
So, the simplified value of [tex]\(|+2| + |+2|\)[/tex] is 4.
### b) [tex]\(|-3| + |+3|\)[/tex]
1. [tex]\(|-3|\)[/tex] represents the absolute value of [tex]\(-3\)[/tex].
2. The absolute value of [tex]\(-3\)[/tex] is [tex]\(3\)[/tex].
3. [tex]\(|+3|\)[/tex] represents the absolute value of [tex]\(+3\)[/tex].
4. The absolute value of [tex]\(+3\)[/tex] is [tex]\(3\)[/tex].
5. Therefore, [tex]\(|-3| + |+3| = 3 + 3 = 6\)[/tex].
So, the simplified value of [tex]\(|-3| + |+3|\)[/tex] is 6.
### c) [tex]\(-7 - |+4|\)[/tex]
1. [tex]\(|+4|\)[/tex] represents the absolute value of [tex]\(+4\)[/tex].
2. The absolute value of [tex]\(+4\)[/tex] is [tex]\(4\)[/tex].
3. Substitute [tex]\(4\)[/tex] into the expression: [tex]\(-7 - 4\)[/tex].
4. Simplify the expression: [tex]\(-7 - 4 = -11\)[/tex].
So, the simplified value of [tex]\(-7 - |+4|\)[/tex] is -11.
### d) [tex]\(|+6| - |-9|\)[/tex]
1. [tex]\(|+6|\)[/tex] represents the absolute value of [tex]\(+6\)[/tex].
2. The absolute value of [tex]\(+6\)[/tex] is [tex]\(6\)[/tex].
3. [tex]\(|-9|\)[/tex] represents the absolute value of [tex]\(-9\)[/tex].
4. The absolute value of [tex]\(-9\)[/tex] is [tex]\(9\)[/tex].
5. Therefore, [tex]\(|+6| - |-9| = 6 - 9\)[/tex].
6. Simplify the expression: [tex]\(6 - 9 = -3\)[/tex].
So, the simplified value of [tex]\(|+6| - |-9|\)[/tex] is -3.
### Summary
The simplified values of the expressions are:
1. [tex]\(|+2| + |+2| = 4\)[/tex]
2. [tex]\(|-3| + |+3| = 6\)[/tex]
3. [tex]\(-7 - |+4| = -11\)[/tex]
4. [tex]\(|+6| - |-9| = -3\)[/tex]
