We have 6x + 5 = 2x + 17 Transposing 2x to L.H.S. and 5 to R.H.S., we get 6x - 2x = 17 - 5 4x = 12 Dividing both sides by 4, we get 4x 4 =12 4 x=3 Verification: Substituting x = 3 in the given equation, we get 6 × 3 + 5 = 2 × 3 + 17 18 + 5 = 6 + 17 23 = 23 L.H.S. = R.H.S. Hence, verified.

6x + 5 = 2x + 17

Two parallel lines $l$ and $m$ are cut by a transversal $t.$ If the interior angles of the same side of t be $(2x - 8)o$ and $(3x - 7)o,$ find the measure of each of these angles.

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Construct an equilateral triangle each of whose sides measures $6.2\ cm$. Measure each of its angles.

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Assume $x$ and $y$ are two negative numbers. The result of the multiplication of $x$ and $y$ with the same positive power is greater than the multiplication of $x$ and $y$ with the same negative power. Give an example to support this statement.

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$14=\frac{7\text{x}}{10}-8$

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Designing a Healthy Diet
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.
$1.$ Calculate your ideal weight as per your height from the table given at the end of this question.
$2.$ An active child should eat around $55.11$ calories for each kilogram desired weight.
$3. \ 55\%$ of calories should come from carbohydrates. There are $4$ calories in each gram of carbohydrates.
$4. \ 15\%$ of your calories should come from proteins. There are $4$ calories in each gram of proteins.
$5. \ 30\%$ of your calories may come from fats. There are $9$ calories in each gram of fats.
Following is an example to design your own healthy diet.
Example:
$1.$ Ideal weight $= 40\ kg.$
$2.$ The number of calories needed $= 40 \times 55.11 = 2204.4$
$3.$ Calories that should come from carbohydrates
$= 2204.4 \times 0.55 = 1212.42$ calories.
Therefore, required quantity of carbohydrates
$=\frac{1212.40}{4}=303.105\text{g}=300\text{g.}$
$4.$ Calories that should come from proteins
$= 2204.4 \times 0.15 = 330.66$ calories.
Therefore, required quantity of protein
$=\frac{330.66}{4}\text{g}=82.66\text{g}.$
$5.$ Calories that may come from fat $= 2204.4 \times 0.3$
$= 661.3$ calories.
Therefore, required quantity of fat
$=\frac{661.3}{9}\text{g}=73.47\text{g.}$
$1.$ Your ideal desired weight is $.......... kg.$
$2.$ The quantity of calories you need to eat is $........g$
$3.$ The quantity of protein needed is $.........g.$
$4.$ The quantity of fat required is $.........g.$
$5.$ The quantity of carbohydrates required is $.........g.$

		Ideal Height and Weight Proportion
	Men			Women
Height		Weight	Height		Weight
Feet	$cm$	Kilograms	Feet	$cm$	Kilograms
$5’$	$152$	$48$	$4’7”$	$140$	$34$
$5’1”$	$155$	$51$	$4’8”$	$142$	$36$
$5’2”$	$157$	$54$	$4’9”$	$145$	$39$
$5’3”$	$160$	$56$	$4’1”$	$147$	$41$
$5’4”$	$163$	$59$	$4’11”$	$150$	$43$
$5’5”$	$165$	$62$	$5’$	$152$	$45$
$5’6”$	$168$	$65$	$5’1”$	$155$	$48$
$5’7”$	$170$	$67$	$5’2”$	$157$	$50$
$5’8”$	$173$	$70$	$5’3”$	$160$	$52$
$5’9”$	$175$	$73$	$5’4”$	$163$	$55$
$5’10”$	$178$	$75$	$5’5”$	$165$	$57$
$5’11”$	$180$	$78$	$5’6”$	$168$	$59$
$6’$	$1834$	$81$	$5’7”$	$170$	$61$
$6’1”$	$185$	$84$	$5’8”4$	$173$	$64$
$6’2”$	$188$	$86$	$5’9”$	$175$	$66$
$6’3”$	$191$	$89$	$5’10”$	$178$	$68$
$6’4”$	$193$	$92$	$5’11”$	$180$	$70$

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In Fig., $A D$ and $C F$ are respectively perpendiculars to sides $B C$ and $A B$ of $\triangle A B C$. If $\angle F C D=50^{\circ}$, find $\angle B A D$.

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Add $2 x^2-3 x+1$ to the sum of $3 x^2-2 x$ and $3 x+7$

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S.No	Column $I$		Column $II$
$i$	$x + 5 = 9$	$a$	$-\frac{5}{3}$
$ii$	$x - 7 = 4$	$b$	$\frac{5}{3}$
$iii$	$\frac{\text{x}}{12}=-5$	$c$	$4$
$iv$	$5x = 30$	$d$	$6$
$v$	The value of y which satisfies $3y = 5$	$e$	$11$
$vi$	If $p = 2$, then the value of $\frac{1}{3}(1-3\text{p})$	$f$	$-60$
		$g$	$3$

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$3x - 2(2x - 5) = 2(x + 3) - 8$

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Evaluate: $\frac{11}{-12}+\frac{3}{-8}+\frac{1}{4}$

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