In the equation, which is true about the value of x? 3x + 7(x + 1) = 2(6x + 5) − 2x
a. no solution
b. one solution
c. infinite solutions
d. x = 7, x = 10

Option A

ANSWER:  

In the equation, 3x+7(x + 1) = 2(6x + 5) -2x ,no solution exists for “x”

SOLUTION:

Given equation is 3x + 7(x + 1) = 2(6x + 5) − 2x

By multiplying the terms within the bracket, we get

3x + 7x + 7 = (2)6x + (2)5 – 2x

On simplifying the above equation, we get

3x + 7x + 7 = 12x +10 -2x

10x + 7 = 10x + 10

By moving the terms from right side to left side, we get

(10x -10x) + (7 – 10) = 0  

0 + (-3) = 0

-3 = 0

Hence the given equation is invalid for any value of x

So, there is no solution, which satisfies the given equation.

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is