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Answer :
Let's solve the inequality [tex]\(-8x + 40 > -16\)[/tex] step-by-step:
1. Add 16 to both sides of the inequality:
[tex]\(-8x + 40 + 16 > 0\)[/tex]
[tex]\(-8x + 56 > 0\)[/tex]
2. Subtract 56 from both sides:
[tex]\(-8x > -56\)[/tex]
3. Divide both sides by -8 and remember to reverse the inequality sign because we're dividing by a negative number:
[tex]\(x < 7\)[/tex]
So, the solution to the inequality [tex]\(-8x + 40 > -16\)[/tex] is [tex]\(x < 7\)[/tex].
The correct multiple-choice option is:
B. [tex]\(x < 7\)[/tex]
1. Add 16 to both sides of the inequality:
[tex]\(-8x + 40 + 16 > 0\)[/tex]
[tex]\(-8x + 56 > 0\)[/tex]
2. Subtract 56 from both sides:
[tex]\(-8x > -56\)[/tex]
3. Divide both sides by -8 and remember to reverse the inequality sign because we're dividing by a negative number:
[tex]\(x < 7\)[/tex]
So, the solution to the inequality [tex]\(-8x + 40 > -16\)[/tex] is [tex]\(x < 7\)[/tex].
The correct multiple-choice option is:
B. [tex]\(x < 7\)[/tex]
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