Let's solve the inequality step-by-step to determine the value of [tex]\( x \)[/tex].
We start with the given inequality:
[tex]\[
-6 \geq 5(x - 2) - 0.7
\][/tex]
### Step 1: Distribute the 5 on the right-hand side
Distribute the 5 inside the parentheses:
[tex]\[
-6 \geq 5x - 10
\][/tex]
Now, we must also subtract the 0.7:
[tex]\[
-6 \geq 5x - 10 - 0.7
\][/tex]
### Step 2: Combine constants on the right-hand side
Combine the constants [tex]\(-10\)[/tex] and [tex]\(-0.7\)[/tex]:
[tex]\[
-6 \geq 5x - 10.7
\][/tex]
### Step 3: Isolate the variable [tex]\( x \)[/tex]
To isolate [tex]\( x \)[/tex], we will first add 10.7 to both sides of the inequality:
[tex]\[
-6 + 10.7 \geq 5x
\][/tex]
[tex]\[
4.7 \geq 5x
\][/tex]
### Step 4: Solve for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], divide both sides by 5:
[tex]\[
\frac{4.7}{5} \geq x
\][/tex]
This simplifies to:
[tex]\[
0.94 \geq x
\][/tex]
or equivalently,
[tex]\[
x \leq 0.94
\][/tex]
### Conclusion
The solution to the inequality [tex]\(-6 \geq 5(x - 2) - 0.7\)[/tex] is:
[tex]\[
x \leq 0.94
\][/tex]
