Respuesta :
• Integer values: ,numbers including 0, and negative and positive numbers; it can never be a fraction, a decimal, or a percent.
Based on the definition, the integer values included in the interval [-5, 0] are: -5, -4, -3, -2, -1, and 0.
To evaluate if the integer satisfies the inequality, we have to evaluate each integer.
• -5
[tex]4\cdot(-5)+7>-9[/tex][tex]-20+7>-9[/tex][tex]-13>-9[/tex]As -13 is smaller than -9, then -5 does not satisfy the inequality.
• -4
[tex]4\cdot(-4)+7>-9[/tex][tex]-16+7>-9[/tex][tex]-9>-9[/tex]As -9 is equal to -9, then -4 does not satisfy the inequality (as in the sign of the inequality it is not included -9).
• -3
[tex]4\cdot(-3)+7>-9[/tex][tex]-12+7>-9[/tex][tex]-5>-9[/tex]As -5 is bigger than -9, -3 satisfies the inequality.
• -2
[tex]4\cdot(-2)+7>-9[/tex][tex]-8+7>-9[/tex][tex]-1>-9[/tex]As -1 is bigger than -9, -2 satisfies the inequality.
• -1
[tex]4\cdot(-1)+7>-9[/tex][tex]-4+7>-9[/tex][tex]3>-9[/tex]As 3 is bigger than -9, -1 satisfies the inequality.
• 0
[tex]4\cdot(0)+7>-9[/tex][tex]7>-9[/tex]As 7 is bigger than -9, 0 satisfies the inequality.
Also we can try by solving the inequality:
[tex]4x+7>-9[/tex][tex]4x>-9-7[/tex][tex]x>\frac{-16}{4}[/tex][tex]x>-4[/tex]Meaning that all the values that are greater than -4 but not -4.
Answer:
• [-3, 0]
,• x = -3, -2, -1, 0
,• x > -4
