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Solve the following inequality:

[tex]\[ -6 \geq 5(x-2) - 0.7 \][/tex]

Answer: ☐


Sagot :

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]
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