5(2 - 3x) - 17(2x - 5) = 16

Question

$5(2 - 3x) - 17(2x - 5) = 16$

✓

Answer

$5(2 - 3x) - 17(2x - 5) = 16$
On expanding the brackets, we get $(5 \times 2) - (5 \times 3x) - (17 \times 2x) + (17 \times 5) $
$= 16 10 - 15x - 34x + 85 $
$= 16 10 + 85 - 34x - 15x $
$= 16 95 - 49x $
$= 16$
Subtracting 95 from both sides, we get $-49x + 95 - 95 = 16 - 95 -49x = -79$
Dividing both sides by $-49,$
we get $\frac{-49\text{x}}{49}=\frac{-79}{-49}$ $\text{x}=\frac{79}{49}$
Verification: Substituting $\text{x}=\frac{79}{49}$ in $L.H.S.,$
we get $=5\Big(2-3\times\frac{79}{49}\Big)-17\Big(2\times\frac{79}{49}-5\Big)$
$=(5\times2)-\Big(5\times3\times\frac{79}{49}\Big)-\Big(17\times2\times\frac{79}{49}\Big)+(17\times5)$
$=10-\frac{1185}{49}-\frac{2686}{49}+85$
$=\frac{490-1185-2686+4165}{49}=\frac{784}{49}=16=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence, verified.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Linear Equations in One Variable→Linear Equations in One Variable — all question types→MATHS STD 7 question papers→Gujarat Board STD 7 question papers→Gujarat Board question paper generator→

Similar questions

Solve the following equations. Check your result in case. $6(3x + 2) - 5(6x - 1) = 3(x - 8) - 5(7x - 6) + 9x$

→

Estimate and then measure the objects listed in the following table. Draw a double bar graph based on the data. How accurate were your estimates? Find the average difference between the estimated and measured values.

Object	Estimate (in cm)	Measure (in cm)	Positive Difference
Length of a pen
Length of an eraser
Length of your plam
Length of your geometry box
Length of your math notebook

→

Evaluate: $\frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$

→

In $\triangle\text{DEF}, \angle\text{D} = 60^\circ , \angle\text{E} = 70^\circ $ and the bisectors of $\angle\text{E}$ and $\angle\text{F}$ meet at $O$. Find $(i) \ \angle\text{F} \ (ii) \ \angle\text{EOF}.$

→

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