MATHEMATICS HIGH SCHOOL

Which inequality has no solution?6(x+2)> x-3

3+4x<2(1+2x)

-2(x+6)< x-20

x-9 < 3 (x-3)

Answers

Answer 1
Answer:

we will proceed to solve all cases to determine the solution of the problem

case A)6(x+2)> x-3

Eliminate the parenthesis of the left side

6x+12> x-3

Group terms that contain the same variable, and move the constants to the opposite side of the inequality

6x-x> -3-12

Combine like terms

5x> -15

x> -3

The solution is the interval--------> (-3,∞)

All real numbers greater than -3

therefore

The inequality A has solution

case B)3+4x <2(1+2x)

Eliminate the parenthesis of the right side

3+4x <2+4x

Group terms that contain the same variable, and move the constants to the opposite side of the inequality

4x-4x <2-3

Combine like terms

0 <-1 ---------> is not true

therefore

The inequality B has no solution

case C)-2(x+6)< x-20

Eliminate the parenthesis of the left side

-2x-12< x-20

Group terms that contain the same variable, and move the constants to the opposite side of the inequality

-2x-x< -20+12

Combine like terms

-3x< -8

Multiply by -1 both sides

3x> 8

x> (8/3)

The solution is the interval--------> (8/3,∞)

All real numbers greater than 8/3

therefore

The inequality C has solution

case D)x-9<3(x-3)

Eliminate the parenthesis of the right side

x-9<3x-9

Group terms that contain the same variable, and move the constants to the opposite side of the inequality

x-3x< -9+9

Combine like terms

-2x< 0

Multiply by -1 both sides

2x> 0

x>0

The solution is the interval--------> (0,∞)

All real numbers greater than 0

therefore

The inequality D has solution

therefore

the answer is

3+4x <2(1+2x)
Answer 2
Answer:

\boxed{3 + 4x < 2\left( {1 + 2x} \right)} inequality has no solution. Option (b) is correct.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

\boxed{y = mx + c}

The formula for slope of line with points \left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}} \right) can be expressed as,

\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}

Given:

The inequalities are as follows,

(a). 6\left( {x + 2} \right) > x - 3

(b). 3 + 4x < 2\left( {1 + 2x} \right)

(c). - 2\left( {x + 6} \right) < x - 20

(d). x - 9 < 3\left( {x - 3} \right)

Explanation:

Solve the inequality 6\left( {x + 2} \right) > x - 3 to check whether the inequality has solution.

\begin{aligned}6\left( {x + 2} \right) >& x - 3\n6x + 12 >& x - 3\n6x - x >&  - 3 - 12\n 5x >&- 15\nx >& \frac{{ - 15}}{5}\nx >&- 3\n\end{aligned}

Option (a) has solution.

Solve the inequality 3 + 4x < 2\left( {1 + 2x} \right) to check whether the inequality has solution.

\begin{aligned}3+ 4x &< 2\left( {1 + 2x} \right)\n3 + 4x &< 2 + 4x\n3&< 2\n\end{aligned}

Option (b) has no solution.

Solve the inequality - 2\left( {x + 6} \right) < x - 20 to check whether the inequality has solution.

\begin{aligned}- 2\left( {x + 6}\right) &< x - 20\n- 2x - 12 &< x - 20\n- 12 + 20 &< x + 2x\n8&< 3x\n(8)/(3) &< x\n\end{aligned}

Option (c) has solution.

Solve the inequality x - 9 < 3\left( {x - 3} \right) to check whether the inequality has solution.

\begin{aligned}x - 9&< 3\left( {x - 3} \right)\nx - 9&< 3x - 9\nx&< 3x \n1&< 3\n\end{aligned}

Option (d) has solution.

\boxed{3 + 4x < 2\left( {1 + 2x} \right)} inequality has no solution. Option (b) is correct.

Learn more:

  1. Learn more about inverse of the functionbrainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers,slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

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Answers

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45 – 15 – 15 =
A. 15.
B. 0.
C. 1.
D. 30

Answers

The result of the expression 45 - 15 - 15 is 15.

(Option A).

What is the solution of the expression?

The solution of the linear expression is calculated as follows;

The given expression;

45 – 15 – 15 = ?

To solve the expression 45 - 15 - 15, we follow the order of operations, which dictates that we perform the subtraction operations from left to right.

First, we subtract 15 from 45:

45 - 15 = 30

Then, we subtract another 15 from the result of the previous operation:

30 - 15 = 15

Therefore, the result of the expression 45 - 15 - 15 is 15.

Therefore, the correct option is A. 15.

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45 - 15 - 15 = 45 - 30

45 - 30 = (15)

a circular fountain has a radius of 9.4 ft find its circumstance to the nearest hundredth using pi over3

Answers

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= 2*3*9.4
=56.4 (to nearest hundredth)

therefore the circumference of the circular fountain is 56.4 feet to the nearest hundredth.  

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Answers

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Answers

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