Respuesta :
1. subtract over the x on the right side of the inequality so you get 4x<16 divide 4 over to get x alone the inequality turns into x<4.
2. subtract over the x on the right side so you get 11x<22 divide over 11 to get x<2
3. Add over 10 to get -8x>7x+30 subtract over 7x to get -15x>30 divide by -15 to get x<-2 make sure to flip over the sign since you're dividing by a negative
4. Add over the 4 to get 13x<12x+3 subtract over 12 and get x<3
5. I can't solve five since their is no inequality sign, the answers show it both ways so i need a starting one to go off on but it is either A or B just flip over the original sign and that will be the answer .
6. Distribute the 7 to get 7x-14<-5 add over the 14 and get 7x<9 divide over the 7 and get x<9/7
2. subtract over the x on the right side so you get 11x<22 divide over 11 to get x<2
3. Add over 10 to get -8x>7x+30 subtract over 7x to get -15x>30 divide by -15 to get x<-2 make sure to flip over the sign since you're dividing by a negative
4. Add over the 4 to get 13x<12x+3 subtract over 12 and get x<3
5. I can't solve five since their is no inequality sign, the answers show it both ways so i need a starting one to go off on but it is either A or B just flip over the original sign and that will be the answer .
6. Distribute the 7 to get 7x-14<-5 add over the 14 and get 7x<9 divide over the 7 and get x<9/7
Answer: The inequalities are solved below.
Step-by-step explanation: We are given to solve the following inequalities:
(1) The first inequality is :
[tex]5x<16+x.[/tex]
The solution is as follows:
[tex]5x<16+x\\\\\Rightarrow 5x-x<16\\\\\Rightarrow 4x<16\\\\\Rightarrow x<4.[/tex]
Thus, (c) x < 4 is the correct solution.
(2) The second inequality is :
[tex]12x<22+x.[/tex]
The solution is as follows:
[tex]12x<22+x\\\\\Rightarrow 12x-x<22\\\\\Rightarrow 11x<22\\\\\Rightarrow x<2.[/tex]
Thus, (c) x < 2 is the correct solution.
(4) The fourth inequality is :
[tex]13x-4<12x-1.[/tex]
The solution is as follows:
[tex]13x-4<12x-1\\\\\Rightarrow 13x-12x<-1+4\\\\\Rightarrow x<3.[/tex]
Thus, (a) x < 3 is the correct solution.
(4) The fourth inequality is :
[tex]13x-4<12x-1.[/tex]
The solution is as follows:
[tex]13x-4<12x-1\\\\\Rightarrow 13x-12x<-1+4\\\\\Rightarrow x<3.[/tex]
Thus, (a) x < 3 is the correct solution.
(5) The fifth inequality is :
[tex]3-5(2x+1)\geq 10.[/tex]
The solution is as follows:
[tex]3-5(2x+1)\geq 10\\\\\Rightarrow 3-10x-5\geq 10\\\\\Rightarrow -10x-2\geq 10\\\\\Rightarrow -10x\geq 12\\\\\Rightarrow 10x\leq -12\\\\\Rightarrow x\leq -\dfrac{6}{5}.[/tex]
Thus, (b) [tex]x\leq -\dfrac{6}{5}[/tex] is the correct solution.
(6) The sixth inequality is :
[tex]7(x-2)<-5.[/tex]
The solution is as follows:
[tex]7(x-2)<-5\\\\\Rightarrow 7x-14<-5\\\\\Rightarrow 7x<-5+14\\\\\Rightarrow 7x<9\\\\\Rightarrow x<\dfrac{9}{7}.[/tex]
Thus, (a) [tex]x<\dfrac{9}{7}[/tex] is the correct solution.
Thus, all the inequalities are solved.
