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3 years ago

Solve the following inequality: 3x + 9 ≤7x -11.

Mathematics

2 answers:

Snowcat [4.5K]3 years ago

7 0

Answer:

5 ≤x

Step-by-step explanation:

3x + 9 ≤7x -11

Subtract 3x from each side

3x-3x + 9 ≤7x-3x -11

9 ≤4x -11

Add 11 to each side

9+11 ≤4x -11+11

20 ≤4x

Divide each side by 4

20/4 ≤4x /4

5 ≤x

m_a_m_a [10]3 years ago

6 0

Answer:

x ≥ -3

Step-by-step explanation:

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

-4x - 12 = -4 • (x + 3)

Equation at the end of step 1 :

Step 2 :

2.1 Divide both sides by -4

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2 Subtract 3 from both sides

x ≥ -3

Inequality Plot :

2.3 Inequality plot for

-4.000 X - 12.000 ≥ 0

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3 years ago

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2 years ago

X2 + 45x = -200 Using the quadratic formual and the discirimnat

dybincka [34]

Answer:

Positive discriminant = 2 real solution

x= -5,-40

Step-by-step explanation:

The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.

The discriminant is the part of the quadratic formula inside the square root:

$b^{2}-4ac$

Every quadratic formula has the structure:

$ax^{2} +bx+c=0$

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

$x^{2} +45x+200=0$

Our a=1, b=45 and c=200

Now we can substitute these values into the discriminant:

$(45)^{2} -4(1)(200)$

Solve:

$2025-800=1225$

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

$x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}$