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1 vote
−9x+5<17 AND 13x+25<−1

User Wwv
by
5.3k points

2 Answers

3 votes

Answer: There are no solutions.

Explanation:

We are given an \maroonC{\text{AND}}ANDstart color #ed5fa6, start text, A, N, D, end text, end color #ed5fa6 statement. A certain xxx-value is a solution of the statement if it satisfies both of the inequalities.

Therefore, the solution of this statement is the intersection of the solutions of both inequalities. In other words, the overlap of the solutions of both inequalities is the solution of the statement.

Finding the solutions to the two inequalities

The solution of the first inequality, -9x+5<17−9x+5<17minus, 9, x, plus, 5, is less than, 17, is x> -\dfrac43x>−

3

4

x, is greater than, minus, start fraction, 4, divided by, 3, end fraction. [Show me the solution process]

\begin{aligned} -9x+5&< 17\\\\ -9x &< 12 \\\\ x &> -\dfrac43 \end{aligned}

The solution of the second inequality, 13x+25<-113x+25<−113, x, plus, 25, is less than, minus, 1, is x<-2x<−2x, is less than, minus, 2.

The inequalities \tealD{x>-\dfrac43}x>−

3

4

start color #01a995, x, is greater than, minus, start fraction, 4, divided by, 3, end fraction, end color #01a995 and \purpleD{x<-2}x<−2start color #7854ab, x, is less than, minus, 2, end color #7854ab are graphed below.

The intersection of the solutions of both inequalities is empty.

User Basim Sherif
by
4.2k points
4 votes

-9x + 5 < 17

To solve this you must isolate x

First subtract 5 to both sides (what you do on one side you must do to the other). Since 5 is being added, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

-9x + 5 - 5 < 17 - 5

-9x < 12

Next divide -9 to both sides to finish isolating x. Since -9 is being multiplied by x, division (the opposite of multiplication) will cancel -9 out (in this case it will make -9 one) from the left side and bring it over to the right side.

-9x/-9 < 12/-9

x > -4/3

OR

x > -1.3333

NOTE!!! When you have an inequality and you are divide a negative number to the opposite side you MUST flip the inequality sign! You will only do this when you are bringing a negative number to the other side of the inequality.

13x + 25 < - 1

To solve this you must isolate x

First subtract 25 to both sides (what you do on one side you must do to the other). Since 25 is being added, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

13x + 25 - 25 < -1 -25

13x < -26

Next divide 13 to both sides to finish isolating x. Since 13 is being multiplied by x, division (the opposite of multiplication) will cancel 13 out (in this case it will make 13 one) from the left side and bring it over to the right side.

13x/13 < -26/13

x < -2

Hope this helped!

~Just a girl in love with Shawn Mendes

User Mihsathe
by
5.2k points