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Answer :
Let's solve the inequality step by step:
Given inequality:
[tex]\[ x \geq x - 2(x + 10) - 7.5 \][/tex]
1. Distribute the -2:
Start by distributing the [tex]\(-2\)[/tex] in the expression [tex]\(-2(x + 10)\)[/tex]:
[tex]\[ -2(x + 10) = -2x - 20 \][/tex]
2. Substitute back into the inequality:
Replace [tex]\(-2(x + 10)\)[/tex] with [tex]\(-2x - 20\)[/tex] in the inequality:
[tex]\[ x \geq x - 2x - 20 - 7.5 \][/tex]
3. Combine like terms:
On the right side, combine the terms:
[tex]\[ x \geq x - 2x - 20 - 7.5 \][/tex]
Simplifies to:
[tex]\[ x \geq -x - 27.5 \][/tex]
4. Isolate x:
To isolate [tex]\(x\)[/tex], add [tex]\(x\)[/tex] to both sides:
[tex]\[ x + x \geq -27.5 \][/tex]
Simplifies to:
[tex]\[ 2x \geq -27.5 \][/tex]
5. Solve for x:
Finally, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x \geq -13.75 \][/tex]
So, the solution to the inequality is:
[tex]\[ x \geq -13.75 \][/tex]
This means [tex]\(x\)[/tex] must be greater than or equal to [tex]\(-13.75\)[/tex].
Given inequality:
[tex]\[ x \geq x - 2(x + 10) - 7.5 \][/tex]
1. Distribute the -2:
Start by distributing the [tex]\(-2\)[/tex] in the expression [tex]\(-2(x + 10)\)[/tex]:
[tex]\[ -2(x + 10) = -2x - 20 \][/tex]
2. Substitute back into the inequality:
Replace [tex]\(-2(x + 10)\)[/tex] with [tex]\(-2x - 20\)[/tex] in the inequality:
[tex]\[ x \geq x - 2x - 20 - 7.5 \][/tex]
3. Combine like terms:
On the right side, combine the terms:
[tex]\[ x \geq x - 2x - 20 - 7.5 \][/tex]
Simplifies to:
[tex]\[ x \geq -x - 27.5 \][/tex]
4. Isolate x:
To isolate [tex]\(x\)[/tex], add [tex]\(x\)[/tex] to both sides:
[tex]\[ x + x \geq -27.5 \][/tex]
Simplifies to:
[tex]\[ 2x \geq -27.5 \][/tex]
5. Solve for x:
Finally, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x \geq -13.75 \][/tex]
So, the solution to the inequality is:
[tex]\[ x \geq -13.75 \][/tex]
This means [tex]\(x\)[/tex] must be greater than or equal to [tex]\(-13.75\)[/tex].
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