Question 1

1. Complete the last column of the table by checking whether the value given in the third column is the solution to the equation in the second column. 2. Check whether the value given in the brackets is a solution to the given equation or not. 3. Solve equations by inspection. 4. Write equations for the given statements involving $x,y,a,b,t,m,z$. 5. Write statements for the given equations. 6. Set up equations for the given word statements.

Accepted Answer

1. (i) No (ii) No (iii) Yes (iv) No (v) Yes (vi) No (vii) Yes (viii) No (ix) No (x) No (xi) Yes. 2. (a) No (b) No (c) Yes (d) No (e) No (f) No. 3. (i) $p=3$ (ii) $m=6$. 4. (i) $x+4=9$ (ii) $y-2=8$ (iii) $10a=70$ (iv) $\frac{b}{5}=6$ (v) $\frac{3t}{4}=15$ (vi) $7m+7=77$ (vii) $\frac{x}{4}-4=4$ (viii) $6y-6=60$ (ix) $\frac{z}{3}+3=30$. 5. (i) The sum of $p$ and 4 is 15. (ii) 7 subtracted from $m$ is 3. (iii) Twice a number $m$ is 7. (iv) One-fifth of a number $m$ is 3. (v) Three-fifth of a number $m$ is 6. (vi) Three times a number $p$ when added to 4 gives 25. (vii) 2 subtracted from four times a number $p$ is 18. (viii) Add 2 to half of a number $p$ to get 8. 6. (i) $5m+7=37$ (ii) $3y+4=49$ (iii) $2l+7=87$ (iv) $4b=180^\circ$.

Question 2

1. Give first the step you will use to separate the variable and then solve the equation. 2. Give the steps you will use to separate the variable and then solve the equation. 3. Solve the equations given in paired form. 4. Solve the listed simple equations involving $p,s,q$.

Accepted Answer

1. (a) Add 1 to both sides; $x=1$ (b) Subtract 1 from both sides; $x=-1$ (c) Add 1 to both sides; $x=6$ (d) Subtract 6 from both sides; $x=-4$ (e) Add 4 to both sides; $y=-3$ (f) Add 4 to both sides; $y=8$ (g) Subtract 4 from both sides; $y=0$ (h) Subtract 4 from both sides; $y=-8$. 2. (a) Divide both sides by 3; $l=14$ (b) Multiply both sides by 2; $b=12$ (c) Multiply both sides by 7; $p=28$ (d) Divide both sides by 4; $x=\frac{25}{4}$ (e) Divide both sides by 8; $y=\frac{36}{8}$ (f) Multiply both sides by 3; $z=\frac{15}{4}$ (g) Multiply both sides by 5; $a=\frac{7}{3}$ (h) Divide both sides by 20; $t=\frac{1}{2}$. 3. (a) Add 2 to both sides, then divide by 3; $n=16$. (b) Subtract 7 from both sides, then divide by 5; $m=2$. (c) Multiply both sides by 3, then divide by 20; $p=6$. (d) Multiply both sides by 10, then divide by 3; $p=20$. 4. (a) $p=10$ (b) $p=9$ (c) $p=20$ (d) $p=-15$ (e) $p=8$ (f) $s=-3$ (g) $s=-4$ (h) $s=0$ (i) $q=3$ (j) $q=3$ (k) $q=-3$ (l) $q=3$.

Question 3

1. Set up equations and solve them to find the unknown numbers in statements (a) to (g). 2. Solve the word problems on lowest score, equal angles, and runs scored by Sachin and Rahul. 3. Solve the given age and number problems. 4. Solve the perimeter problem in the exercise.

Accepted Answer

1. (a) $8x+4=60$, $x=7$ (b) $\frac{x}{5}-4=3$, $x=35$ (c) $\frac{3y}{4}+3=21$, $y=24$ (d) $2m-11=15$, $m=13$ (e) $50-3x=8$, $x=14$ (f) $\frac{x+19}{5}=8$, $x=21$ (g) $\frac{5n}{2}-7=23$, $n=12$. 2. (a) Lowest score $=40$ (b) $70^\circ$ each (c) Sachin: 132 runs, Rahul: 66 runs. 3. (i) 6 (ii) 15 years (iii) 25. 4. 30.