Question

PLEASE HELP WITH MATH!!!!!!! 60 points and brainliest!!!!!!

1. Solve the inequality 5x < 16 + x.

x < 1/4
x > 1/4
x < 4
x > 4 (not the answer)
2. Solve the inequality 12x < 22 + x.

x < 1/2
x > 1/2 (not the answer)
x < 2
x > 2
3. Solve the inequality -8x - 10 > 7x + 20.

x < - 30
x > - 2
x > - 30 (not the answer)
x < - 2
4. Solve the inequality 13x - 4 < 12x - 1.

x < 3
x > 3
x < 5 (not the answer)
x > 5
5. Solve the inequality 3 - 5(2x + 1) 10.
(picture below!!!) but it's not the answer I selected.
6. Solve the inequality 7(x - 2) < -5.

x < 9/7
x > 9/7
x < -9/7
x > -9/7

Answer 1

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

Answer 2

Answer:  The inequalities are solved below.

Step-by-step explanation:  We are given to solve the following inequalities:

(1) The first inequality is :

$5x<16+x.$

The solution is as follows:

$5x<16+x\\\\\Rightarrow 5x-x<16\\\\\Rightarrow 4x<16\\\\\Rightarrow x<4.$

Thus, (c) x < 4 is the correct solution.

(2) The second inequality is :

$12x<22+x.$

The solution is as follows:

$12x<22+x\\\\\Rightarrow 12x-x<22\\\\\Rightarrow 11x<22\\\\\Rightarrow x<2.$

Thus, (c) x < 2 is the correct solution.

(4) The fourth inequality is :

$13x-4<12x-1.$

The solution is as follows:

$13x-4<12x-1\\\\\Rightarrow 13x-12x<-1+4\\\\\Rightarrow x<3.$

Thus, (a) x < 3 is the correct solution.

(4) The fourth inequality is :

$13x-4<12x-1.$

The solution is as follows:

$13x-4<12x-1\\\\\Rightarrow 13x-12x<-1+4\\\\\Rightarrow x<3.$

Thus, (a) x < 3 is the correct solution.

(5) The fifth inequality is :

$3-5(2x+1)\geq 10.$

The solution is as follows:

$3-5(2x+1)\geq 10\\\\\Rightarrow 3-10x-5\geq 10\\\\\Rightarrow -10x-2\geq 10\\\\\Rightarrow -10x\geq 12\\\\\Rightarrow 10x\leq -12\\\\\Rightarrow x\leq -\dfrac{6}{5}.$

Thus, (b) $x\leq -\dfrac{6}{5}$ is the correct solution.

(6) The sixth inequality is :

$7(x-2)<-5.$

The solution is as follows:

$7(x-2)<-5\\\\\Rightarrow 7x-14<-5\\\\\Rightarrow 7x<-5+14\\\\\Rightarrow 7x<9\\\\\Rightarrow x<\dfrac{9}{7}.$

Thus, (a) $x<\dfrac{9}{7}$ is the correct solution.

Thus, all the inequalities are solved.