Answer:
[tex]\sf D. \quad t < -4, t > 5[/tex]
Step-by-step explanation:
Given system of inequalities:
[tex]\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}[/tex]
Solve the inequalities by isolating t.
Inequality 1
[tex]\sf \implies 5t-1 < -21[/tex]
[tex]\implies \sf 5t-1+1 < -21+1[/tex]
[tex]\sf \implies 5t < -20[/tex]
[tex]\sf \implies 5t \div 5 < -20 \div 5[/tex]
[tex]\sf \implies t < -4[/tex]
Inequality 2
[tex]\sf \implies 4t+2 > 22[/tex]
[tex]\sf \implies 4t+2-2 > 22-2[/tex]
[tex]\sf \implies 4t > 20[/tex]
[tex]\sf \implies 4t \div 4 > 20 \div 4[/tex]
[tex]\sf \implies t > 5[/tex]
Therefore, the solution to the system of inequities is:
[tex]\sf t < -4, t > 5[/tex]
When graphing inequalities:
- < or > : dashed lines
- ≤ or ≥ : solid line
- < or ≤ : shading under the line
- > or ≥ : shading above the line
Therefore, to graph the given system of inequalities:
- Draw a straight dashed line at t = -4 and shade under the line.
- Draw a straight dashed line at t = 5 and shade above the line.
(Refer to attachment for the graph).
Learn more about inequalities here:
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