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How do you solve and graph #10x + 9 > 3x - 1#?

Answer 1

Isaiah Anthony

#x > -10/7#
graph{10x+9 > 3x-1 [-7.9, 7.9, -3.95, 3.95]}

#10x+9 > 3x-1#

#rarrcolor(white)("XXX")10x > 3x -10#

#rarrcolor(white)("XXX")7x > -10#

#rarrcolor(white)("XXX")x > - 10/7#

To graph (on the Cartesian plane) draw a dashed vertical line (dashed to indicate that values on the line are not included in the solution set) at #x=-10/7#; then shade the area to the right (where #x > -10/7#) to indicate inclusion in the solution set.

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Answer 2

Ethan Adkins

To solve and graph the inequality 10x + 9 > 3x - 1:

Subtract 3x from both sides to isolate the variable term: 10x + 9 - 3x > 3x - 1 - 3x 7x + 9 > -1
Subtract 9 from both sides: 7x + 9 - 9 > -1 - 9 7x > -10
Divide both sides by 7: (7x)/7 > (-10)/7 x > -10/7

So, the solution to the inequality is x > -10/7.

To graph this solution on a number line, you draw an open circle at -10/7 (since it's not included in the solution) and shade the region to the right of -10/7, indicating that all values greater than -10/7 satisfy the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph #10x + 9 &gt; 3x - 1#?

How do you solve and graph #10x + 9 > 3x - 1#?