Solve the inequality and graph its solution: –14 < 7t < 21

The solution of the inequality is -2 < t < 3 and the graph is the attachments

Step-by-step explanation:

In order to solve this inequality you can use this rule if a < u < b then a < u and u < b, so -14 < 7t and 7t < 21.

The first inequality:

-14 < 7t = 7t > -14 = 7t/7 > -14/7 = t > -2

The second inequality:

7t < 21 = 7t/7 < 21/7 = t < 3

Merge overlapping intervals gives you the solution:

-2 < t < 3

The solution to this inequality is the set of all real numbers t that are less than 3, and greater than -2 not including -2 and 3. The solution is represented by a line.

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step-by-step explanation:

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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