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Answer :
To solve the inequality [tex]\(-6x + 175 \geq 151\)[/tex], let's break it down step by step:
1. Isolate the variable term: Start by getting the term with the variable on one side, and constants on the other side. To do this, subtract 175 from both sides of the inequality:
[tex]\[
-6x + 175 - 175 \geq 151 - 175
\][/tex]
Simplifying both sides gives us:
[tex]\[
-6x \geq -24
\][/tex]
2. Solve for [tex]\(x\)[/tex]: Now, we need to solve for [tex]\(x\)[/tex]. Since we have a coefficient of [tex]\(-6\)[/tex] with our [tex]\(x\)[/tex], divide both sides of the inequality by [tex]\(-6\)[/tex].
Remember, dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. So, dividing by [tex]\(-6\)[/tex], we get:
[tex]\[
x \leq \frac{-24}{-6}
\][/tex]
Simplifying the right side gives:
[tex]\[
x \leq 4
\][/tex]
3. Solution: This means that the solution to the inequality is all real numbers [tex]\(x\)[/tex] that are less than or equal to 4. In interval notation, this is expressed as:
[tex]\[
(-\infty, 4]
\][/tex]
Thus, [tex]\(x\)[/tex] can be any value up to and including 4.
1. Isolate the variable term: Start by getting the term with the variable on one side, and constants on the other side. To do this, subtract 175 from both sides of the inequality:
[tex]\[
-6x + 175 - 175 \geq 151 - 175
\][/tex]
Simplifying both sides gives us:
[tex]\[
-6x \geq -24
\][/tex]
2. Solve for [tex]\(x\)[/tex]: Now, we need to solve for [tex]\(x\)[/tex]. Since we have a coefficient of [tex]\(-6\)[/tex] with our [tex]\(x\)[/tex], divide both sides of the inequality by [tex]\(-6\)[/tex].
Remember, dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. So, dividing by [tex]\(-6\)[/tex], we get:
[tex]\[
x \leq \frac{-24}{-6}
\][/tex]
Simplifying the right side gives:
[tex]\[
x \leq 4
\][/tex]
3. Solution: This means that the solution to the inequality is all real numbers [tex]\(x\)[/tex] that are less than or equal to 4. In interval notation, this is expressed as:
[tex]\[
(-\infty, 4]
\][/tex]
Thus, [tex]\(x\)[/tex] can be any value up to and including 4.
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