A student solves the equation StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction using the steps

Question

2 years ago

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A student solves the equation StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction using the steps

in the table.
Original equation
StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction
Cross multiplication
5 (x + 3) = 2 (3x + 5)
Distributive property
5 x + 15 = 2 (3 x + 5)
Subtraction property of equality
5 = x

Which method of solving for the variable could be used instead of cross multiplication?
distributing x + 3 and then 3x + 5 to both sides of the equation
distributing x – 3 and then 3x – 5 to both sides of the equation
using the multiplication property of equality to multiply both sides of the equation by 10
using the multiplication property of equality to multiply both sides of the equation by One-tenth

Mathematics

1 answer:

bonufazy [111] · Answer 1 · 2022-05-29T09:41:42+03:00

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

Given equation is:

$\frac{x+3}{2} = \frac{3x+5}{5}$

One method to solve this equation is cross-multiplication which the student has used.

One of the alternate method can be multiplying both sides by the LCM of numerators of fractions on both sides

So multiplying both sides by 10 (multiplication property of equality)

$\frac{x+3}{2} * 10 = \frac{3x+5}{5} * 10\\5(x+3) = 2(3x+5)\\5x+15 = 6x+10\\5x+15-10 = 6x\\6x = 5x+5\\6x-5x = 5\\x = 5$

The alternate method of LCM produces the same answer so the correct answer is:

using the multiplication property of equality to multiply both sides of the equation by 10

Keywords: Linear equations, variables

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