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MrRissso [65]
3 years ago
11

Anna and Belle are asked to solve −2x − 15 = 6x + 9. Identify where one of them made an error. Anna Belle −2x − 15 = 6x + 9 −2x

− 15 −6x = 6x + 9 −6x −8x − 15 = 9 −8x − 15 + 15 = 9 + 15 −8x = 24 Negative 8x over negative 8 equals 24 over negative 8 x = −3 −2x − 15 = 6x + 9 −2x − 15 + 2x = 6x + 9 + 2x −15 = 8x + 9 −15 + 9 = 8x + 9 + 9 −6 = 8x Negative 6x over 8 equals 8x over 8 Negative two-thirds
Mathematics
2 answers:
GalinKa [24]3 years ago
7 0

Answer:

<h2>Belle is wrong.</h2>

Step-by-step explanation:

The given expression is

-2x-15=6x+9

The steps Anna did are

-2x-15=6x+9\\-2x-15-6x=6x+9-6x\\-8x-15=9\\-8x-15+15=9+15\\-8x=24\\\frac{-8x}{-8}=\frac{24}{-8}  \\x=-3

If you look carefuly, you would notice that Anna didn't make any mistakes, her steps and result is correct.

Belle steps are

-2x-15=6x+9\\-2x-15+2x=6x+9+2x\\-15=8x+9\\-15+9=8x+9+9

Notice that this step is wrong, because she's not adding -9 to eliminate that term.

-6=8x, this step is also wrong, because 9 + 9 = 18.

Therefore, Belle is wrong.

Finger [1]3 years ago
5 0

Belle got it wrong when she added the 9 because it was already positive, meaning she would’ve subtracted it.

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Ella has 0.5 lb of sugar. how much water should she add to make the following concentrations? Tell Ella how much syrup she will
makkiz [27]

Answer:

For 50% syrup, add 0.5 lb of water for 1 lb of syrup; for 5% syrup, add 9.5 lb of water for 10 lb of syrup; for 75% syrup, add 0.17 lb of water for 0.67 lb of syrup; for 1.5% syrup, add 32.8 lb of water for 33.3 lb of syrup.

Step-by-step explanation:

Let x represent the amount of water added.  This means the total mass of the syrup is represented by 0.5+x.

To find percentages, we divide the part by the whole.  For a 50% syrup, we need the part (sugar) compared to the whole (sugar + water) to equal 50%, or 0.50:

Multiply both sides by 0.5+x:

Using the distributive property, we have

0.5 = 0.5(0.5)+0.5(x)

0.5 = 0.25+0.5x

Subtract 0.25 from each side:

0.5-0.25 = 0.25+0.5x-0.25

0.25 = 0.5x

Divide both sides by 0.5:

0.25/0.5 = 0.5x/0.5

x = 0.5

For 50% syrup, add 0.5 lb of water.  This makes the total mass 0.5+0.5 = 1 lb.

For 5% syrup, we change the equation to equal 0.05 (5% = 5/100 = 0.05) and leave everything else the same:

Multiply both sides by 0.5+x:

Using the distributive property,

0.5 = 0.05(0.5)+0.05(x)

0.5 = 0.025 + 0.05x

Subtract 0.025 from both sides:

0.5-0.025 = 0.025+0.05x-0.025

0.475 = 0.05x

Divide both sides by 0.05:

0.475/0.05 = 0.05x/0.05

x = 9.5

For 5% syrup, add 9.5 lb of water; the total mass will be 9.5+0.5 = 10 lb.

For 75% syrup, set the equation equal to 0.75:

Using the distributive property,

0.5 = 0.75(0.5)+0.75(x)

0.5 = 0.375 + 0.75x

Subtract 0.375 from each side:

0.5 - 0.375 = 0.375 + 0.75x - 0.375

0.125 = 0.75x

Divide both sides by 0.75:

0.125/0.75 = 0.75x/0.75

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For 75% syrup, add 0.17 lb of water; the total mass is 0.17+0.5 = 0.67 lb.

For 1.5% syrup, set the equation equal to 0.015:

Using the distributive property,

0.5 = 0.015(0.5) + 0.015(x)

0.5 = 0.0075 + 0.015x

Subtract 0.0075 from each side:

0.5-0.0075 = 0.0075 + 0.015x - 0.0075

0.4925 = 0.015x

Divide both sides by 0.015:

0.4925/0.015 = 0.015x/0.015

32.8 = x

For 1.5% syrup, use 32.8 lb of water; the total mass is 32.8+0.5 = 33.3 lb.

I hope this is right and have a good day

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