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Ludmilka [50]
1 year ago
6

What is 2x + 4 < 16

Mathematics
1 answer:
harina [27]1 year ago
7 0

Answer:

x<6         just letting you know that / is not meant for division it means a fraction bar

Step-by-step explanation:

1. Group all constants on the right side of the inequality

2x+4<16

Subtract  from both sides

(2x+4)-4<16-4

Simplify the arithmetic

2x<16-4

Simplify the arithmetic

2x<12

2. Isolate the x

2x<12

Divide both sides by 2

(2x)/2<12/2

Simplify the fraction

x<12/2

Find the greatest common factor of the numerator and denominator

x<6*2/1*2

Factor out and cancel the greatest common factor

x<6

3. Solution on a coordinate plane

Solution: x<6

Interval notation:

(-∞,6)

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Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;5x-4=-2 \times 3x-2 \times 2 \\&#10;5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\&#10;11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\&#10;11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\&#10;x=0

B.
3(2x-4)=5x-1 \\&#10;6x-12=5x-1 \\&#10;\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\&#10;11x=11 \\&#10;\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\&#10;x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\&#10;x=11
3 0
2 years ago
Is the graph of 6x2 - 2y = 7 a line? Explain.
Hoochie [10]

Answer:

No, it is a parabola. (assuming that you meant to write 6x² - 2y = 7).

Step-by-step explanation:

If there is a square in the x or y, this gives it away that it cannot be a straight line.

6 0
3 years ago
Solve the following 3x + 7 = 2x + 13 over 3
yulyashka [42]
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3 0
2 years ago
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Answer:

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Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A car painting company has determined that the painting time of cars is uniformly distributed between 25 and 105 minutes. What i
Masteriza [31]

Answer:

P=\frac{5}{16}

Step-by-step explanation:

For a uniform distribution we have to:

P (X\leq x) =\frac{x-a}{b-a}   for x∈ (a, b)

P (X\leq x) =0}   for x\leq a

P (X\leq x) =1}   for x\geq b

In this case we have to:

a = 25 min and b = 105 min

We want to find:

P (40 \leq X \leq 65)

Then

P (x_1 \leq X \leq x_2) = P(X \leq x_2) - P(X \leq x_1)

P (x_1 \leq X \leq x_2)= \frac{x_2 -x_1}{b-a}

In this case:

x_2 = 65\\\\x_1=40

Therefore:

P (40 \leq X \leq 65)=\frac{65 -40}{105-25}

P (40 \leq X \leq 65)=\frac{25}{80}

P (40 \leq X \leq 65)=\frac{5}{16}

4 0
2 years ago
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