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2 years ago

How many solutions exist for the given equation? 3(x - 2) = 22 -x

Mathematics

2 answers:

alexgriva [62]2 years ago

7 0

There is only one solution because it is a linear equation.
3x - 6 = 22 - x
3x + x = 22 + 6
4x = 28
X = 7

Sveta_85 [38]2 years ago

6 0

Answer:

One solution

Step-by-step explanation:

The equation can be rewrite as 3x - 6 = 22 - x

so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7

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Please answer this question

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As it is given :

Present age of mom : Present age of son = 6 : 1

Therefore let :

Mother's age be 6x

Son's age be x

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Son's age = x + 10

<h3>Part three :</h3>

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Which means :

Mom's age after 10 years : Son's age after 10 years = 8 :3.

Now :

$\scriptsize \purple{ \boxed{ \scriptsize \dfrac{ \text{Mom's age after 10 years}}{ \text{son's age after 10 years}}= \dfrac{8}{3} }} \star$

$\\ \\$

So :

$\small\sf \dashrightarrow \dfrac{6x + 10}{x + 10} = \sf \dfrac{8}{3}$

$\\ \\$

$\small\sf \dashrightarrow \dfrac{3(6x + 10)}{x + 10} = \sf \dfrac{8}{1}$

$\\ \\$

$\small \sf \dashrightarrow \dfrac{18x +30}{x + 10} = \sf \dfrac{8}{1}$

$\\ \\$

$\small\sf \dashrightarrow \dfrac{18x +30}{1} = \sf \dfrac{8(x + 10)}{1}$

$\\ \\$

$\small \sf \dashrightarrow 18x +30= \sf 8(x + 10)$

$\\ \\$

$\small\sf \dashrightarrow 18x +30= \sf 8x + 80$

$\\ \\$

$\small\sf \dashrightarrow 18x - 8x +30= \sf 80$

$\\ \\$

$\small \sf \dashrightarrow 10x +30= \sf 80$

$\\ \\$

$\small \sf \dashrightarrow 10x = \sf 80 - 30$

$\\ \\$

$\small \sf \dashrightarrow 10x = \sf 50$

$\\ \\$

$\small \sf \dashrightarrow \dfrac{10x}{10} = \sf \dfrac{50}{10}$

$\\ \\$

$\small \sf \dashrightarrow \dfrac{1\cancel0x}{1\cancel0} = \sf \dfrac{5\cancel0}{1\cancel0}$

$\\ \\$

$\small\bf \dashrightarrow x = \pink 5$

$\\$

We know :

$\footnotesize \hookrightarrow \sf Son's \: age = x$

$\footnotesize \hookrightarrow \sf Son's \: age = \red{5 \: years}$

$\\ \\$

$\footnotesize \hookrightarrow \sf Mother's \: age = 6x$

$\footnotesize\hookrightarrow \sf Mother's \: age = 6 \times 5$

$\footnotesize \hookrightarrow \sf Mother's \: age = \bf \red{30 \: years}$

And all we are done ! ㋛

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